Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
11422 conjugacy classes of subgroups; only the 3659 normal subgroups are shown.
This group has 11422 conjugacy classes of subgroups — too many to draw. Only its 3659 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#11929625 | C2 | semidirect |
| 2. C22×#14579184 | C2 | direct (N × H) |
| 3. C23×#11929611 | C2 | semidirect |
| 4. C23×D632 | C2 | semidirect |
| 5. C23×C8×D79 | C2 | semidirect |
| 6. C23×Q16×C79 | C2 | semidirect |
| 8. C22×#11929625 | C22 | semidirect |
| 13. C2×#14579184 | C22 | direct (N × H) |
| 14. C22×#11929611 | C22 | semidirect |
| 15. C22×D632 | C22 | semidirect |
| 17. C22×C8×D79 | C22 | semidirect |
| 19. C22×Q16×C79 | C22 | semidirect |
| 24. C2×#11929625 | C23 | semidirect |
| 32. #14579184 | C23 | direct (N × H) |
| 33. C2×#11929611 | C23 | semidirect |
| 34. C2×D632 | C23 | semidirect |
| 36. C2×C8×D79 | C23 | semidirect |
| 41. C2×Q16×C79 | C23 | semidirect |
| 48. #11929625 | C24 | semidirect |
| 56. #11929611 | C24 | semidirect |
| 57. D632 | C24 | semidirect |
| 59. C8×D79 | C24 | semidirect |
| 66. Q16×C79 | C24 | semidirect |
| 68. C23×C79 | #135 | semidirect |
| 88. C22×C79 | C2×#135 | semidirect |
| 99. C2×C79 | C22×#135 | semidirect |
| 105. C23×Q16 | D79 | semidirect |
| 109. C79 | C23×#135 | semidirect |
| 118. C22×Q16 | C2×D79 | semidirect |
| 140. C2×Q16 | C22×D79 | semidirect |
| 165. Q16 | C23×D79 | semidirect |
| 175. C23 | #14579184 | direct (N × H) |
| 195. C22 | C2×#14579184 | direct (N × H) |
| 203. C2 | C22×#14579184 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11929625 | 2 |
| C22×#14579184 | 2 |
| C23×#11929611 | 2 |
| C23×D632 | 2 |
| C23×C8×D79 | 2 |
| C23×Q16×C79 | 2 |
| C23×#135 | 79 |