Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
500 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 217 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. C8×D724 | C2 | semidirect |
| 3. #26041344 | C2 | semidirect |
| 4. #26041332 | C2 | semidirect |
| 5. C22⋊C8×D181 | C2 | semidirect |
| 6. #431×C181 | C2 | semidirect |
| 9. C2×C8×D181 | C22 | semidirect |
| 16. C4⋊#13089678 | C22 | semidirect |
| 18. #19153728 | C22 | semidirect |
| 19. C4×#13089678 | C22 | semidirect |
| 21. C4⋊C8×C181 | C22 | semidirect |
| 23. C4×C8×C181 | C22 | semidirect |
| 25. C2×D724 | C8 | semidirect |
| 48. C22×D181 | C2×C8 | semidirect |
| 50. D724 | C2×C8 | semidirect |
| 51. D724 | C2×C8 | semidirect |
| 60. C2×C4×C181 | C2×C8 | semidirect |
| 88. C181 | #2972 | semidirect |
| 94. #431 | D181 | semidirect |
| 107. C4⋊C8 | C2×D181 | semidirect |
| 112. C4×C8 | C2×D181 | semidirect |
| 148. C2×C4 | C8×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D724 | 2 |
| C8×D724 | 2 |
| #26041344 | 2 |
| #26041332 | 2 |
| C22⋊C8×D181 | 2 |
| #431×C181 | 2 |
| #2972 | 181 |