Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #26041829 | C2 | semidirect |
| 2. #26041592 | C2 | semidirect |
| 3. #26041559 | C2 | semidirect |
| 4. #26041474 | C2 | semidirect |
| 5. #26041413 | C2 | semidirect |
| 6. C4×#15668434 | C2 | semidirect |
| 7. #26041332 | C2 | semidirect |
| 8. C2×C4×D4×C181 | C2 | semidirect |
| 11. #19153816 | C22 | semidirect |
| 12. #19153813 | C22 | semidirect |
| 17. C4×D724 | C22 | semidirect |
| 18. #19153749 | C22 | semidirect |
| 19. C4⋊#13089678 | C22 | semidirect |
| 21. #19153736 | C22 | semidirect |
| 23. C4×#13089678 | C22 | semidirect |
| 81. D4×C181 | #41 | semidirect |
| 88. C2×C4×C181 | D8 | semidirect |
| 120. C181 | #3100 | semidirect |
| 123. C2×C4×D4 | D181 | semidirect |
| 199. D4 | #15668449 | semidirect |
| 208. C2×C4 | #15668434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041829 | 2 |
| #26041592 | 2 |
| #26041559 | 2 |
| #26041474 | 2 |
| #26041413 | 2 |
| C4×#15668434 | 2 |
| #26041332 | 2 |
| C2×C4×D4×C181 | 2 |
| #3100 | 181 |