Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041857 | C2 | semidirect |
| 2. #26041610 | C2 | semidirect |
| 3. #26041598 | C2 | semidirect |
| 4. #26041537 | C2 | semidirect |
| 5. #26041532 | C2 | semidirect |
| 6. #26041508 | C2 | semidirect |
| 7. #26041443 | C2 | semidirect |
| 8. #26041426 | C2 | semidirect |
| 9. #408×C181 | C2 | semidirect |
| 117. C181 | #3204 | semidirect |
| 127. #408 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041857 | 2 |
| #26041610 | 2 |
| #26041598 | 2 |
| #26041537 | 2 |
| #26041532 | 2 |
| #26041508 | 2 |
| #26041443 | 2 |
| #26041426 | 2 |
| #408×C181 | 2 |
| #3204 | 181 |