Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 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. #26041758 | C2 | semidirect |
| 3. #26041391 | C2 | semidirect |
| 4. #26041387 | C2 | semidirect |
| 5. #26041385 | C2 | semidirect |
| 6. #26041370 | C2 | semidirect |
| 7. C4×#15668437 | C2 | semidirect |
| 8. #106×D181 | C2 | semidirect |
| 9. #26041277 | C2 | semidirect |
| 10. #26041236 | C2 | semidirect |
| 11. #442×C181 | C2 | semidirect |
| 13. #19153835 | C4 | semidirect |
| 41. #15668448 | C2×C4 | semidirect |
| 48. Dic724 | C2×C4 | semidirect |
| 49. #15668437 | C2×C4 | semidirect |
| 53. C8×D181 | C2×C4 | semidirect |
| 66. D8×C181 | C2×C4 | semidirect |
| 114. C181 | #2952 | semidirect |
| 119. #442 | D181 | semidirect |
| 167. D8 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153835 | 2 |
| #26041758 | 2 |
| #26041391 | 2 |
| #26041387 | 2 |
| #26041385 | 2 |
| #26041370 | 2 |
| C4×#15668437 | 2 |
| #106×D181 | 2 |
| #26041277 | 2 |
| #26041236 | 2 |
| #442×C181 | 2 |
| #2952 | 181 |