Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
436 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26041830 | C2 | semidirect |
| 2. #26041826 | C2 | semidirect |
| 3. #26041558 | C2 | semidirect |
| 4. #26041556 | C2 | semidirect |
| 5. #26041516 | C2 | semidirect |
| 6. #26041514 | C2 | semidirect |
| 7. #26041475 | C2 | semidirect |
| 8. #26041474 | C2 | semidirect |
| 9. #26041473 | C2 | semidirect |
| 10. C4⋊C8×D181 | C2 | semidirect |
| 11. #474×C181 | C2 | semidirect |
| 107. C4×D181 | D8 | semidirect |
| 150. C181 | #3245 | semidirect |
| 156. #474 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041830 | 2 |
| #26041826 | 2 |
| #26041558 | 2 |
| #26041556 | 2 |
| #26041516 | 2 |
| #26041514 | 2 |
| #26041475 | 2 |
| #26041474 | 2 |
| #26041473 | 2 |
| C4⋊C8×D181 | 2 |
| #474×C181 | 2 |
| #3245 | 181 |