Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
1048 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 181 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×D724 | C2 | semidirect |
| 2. C22×D1448 | C2 | semidirect |
| 3. C2×#19153790 | C2 | semidirect |
| 4. #26041415 | C2 | direct (N × H) |
| 5. C2×#19153738 | C2 | semidirect |
| 6. C2×C22⋊C8×C181 | C2 | semidirect |
| 12. C22×D724 | C22 | semidirect |
| 13. C22×D724 | C22 | semidirect |
| 16. C2×D1448 | C22 | semidirect |
| 18. #19153790 | C22 | semidirect |
| 19. C2×C4⋊Dic181 | C22 | semidirect |
| 21. #19153738 | C22 | semidirect |
| 23. C22×C8×C181 | C22 | semidirect |
| 24. C22⋊C8×C181 | C22 | semidirect |
| 39. C2×D724 | D4 | semidirect |
| 41. C2×D724 | C23 | semidirect |
| 47. C4⋊Dic181 | C23 | semidirect |
| 56. C2×C8×C181 | C23 | semidirect |
| 74. D724 | C2×D4 | semidirect |
| 80. C23×C181 | D8 | semidirect |
| 96. C22×C181 | C2×D8 | semidirect |
| 113. C2×C181 | #447 | semidirect |
| 119. C181 | C2×#447 | semidirect |
| 126. C2×C22⋊C8 | D181 | semidirect |
| 138. C22×C8 | C2×D181 | semidirect |
| 144. C22⋊C8 | C2×D181 | semidirect |
| 173. C2×C8 | C22×D181 | semidirect |
| 191. C23 | D1448 | semidirect |
| 225. C22 | C2×D1448 | semidirect |
| 235. C2 | #26041415 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D724 | 2 |
| C22×D1448 | 2 |
| C2×#19153790 | 2 |
| #26041415 | 2 |
| C2×#19153738 | 2 |
| C2×C22⋊C8×C181 | 2 |
| C2×#447 | 181 |