Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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. #26042045 | C2 | semidirect |
| 3. #26041402 | C2 | semidirect |
| 4. #26041397 | C2 | semidirect |
| 5. #26041328 | C2 | semidirect |
| 6. C2×#19153744 | C2 | semidirect |
| 7. C4×M16×C181 | C2 | semidirect |
| 9. #19153849 | C4 | semidirect |
| 10. #19153844 | C4 | semidirect |
| 13. #19153822 | C22 | semidirect |
| 16. #19153752 | C22 | semidirect |
| 17. #19153744 | C22 | semidirect |
| 18. #19153744 | C22 | semidirect |
| 22. #97×C181 | C22 | semidirect |
| 23. C4×C8×C181 | C22 | semidirect |
| 32. Dic724 | C2×C4 | semidirect |
| 33. #15668438 | C2×C4 | semidirect |
| 34. D1448 | C2×C4 | semidirect |
| 85. C181 | #2956 | semidirect |
| 93. C4×M16 | D181 | semidirect |
| 108. #97 | C2×D181 | semidirect |
| 109. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042079 | 2 |
| #26042045 | 2 |
| #26041402 | 2 |
| #26041397 | 2 |
| #26041328 | 2 |
| C2×#19153744 | 2 |
| C4×M16×C181 | 2 |
| #2956 | 181 |