Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
3614 conjugacy classes of subgroups; only the 2283 normal subgroups are shown.
This group has 3614 conjugacy classes of subgroups — too many to draw. Only its 2283 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 |
|---|---|---|
| 2. C22×#14579093 | C2 | direct (N × H) |
| 7. C2×#14579093 | C22 | direct (N × H) |
| 9. C23×C8×C79 | C4 | semidirect |
| 15. #14579093 | C23 | direct (N × H) |
| 21. C22×C8×C79 | C2×C4 | semidirect |
| 35. C2×C8×C79 | C22×C4 | semidirect |
| 37. C23×C79 | #106 | semidirect |
| 48. C8×C79 | C23×C4 | semidirect |
| 49. C22×C79 | C2×#106 | semidirect |
| 58. C2×C79 | C22×#106 | semidirect |
| 64. C79 | C23×#106 | semidirect |
| 67. C23×C8 | Dic79 | semidirect |
| 79. C22×C8 | C2×Dic79 | semidirect |
| 94. C2×C8 | C22×Dic79 | semidirect |
| 98. C23 | #14579093 | direct (N × H) |
| 109. C8 | C23×Dic79 | semidirect |
| 110. C22 | C2×#14579093 | direct (N × H) |
| 118. C2 | C22×#14579093 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4⋊Dic79 | 2 |
| C22×#14579093 | 2 |
| C24×C8×C79 | 2 |
| C23×#106 | 79 |