Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26042092 | C2 | semidirect |
| 2. #26041721 | C2 | semidirect |
| 3. #26041720 | C2 | semidirect |
| 4. #26041712 | C2 | semidirect |
| 5. #26041711 | C2 | semidirect |
| 6. Q32×D181 | C2 | semidirect |
| 7. #26041695 | C2 | semidirect |
| 8. C2×Q32×C181 | C2 | semidirect |
| 81. C181 | #3417 | semidirect |
| 89. C2×Q32 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042092 | 2 |
| #26041721 | 2 |
| #26041720 | 2 |
| #26041712 | 2 |
| #26041711 | 2 |
| Q32×D181 | 2 |
| #26041695 | 2 |
| C2×Q32×C181 | 2 |
| #3417 | 181 |