Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#19153816 | C2 | semidirect |
| 3. #26041688 | C2 | semidirect |
| 4. #26041639 | C2 | semidirect |
| 5. #26041615 | C2 | semidirect |
| 7. #26041565 | C2 | semidirect |
| 8. #26041560 | C2 | semidirect |
| 9. #432×C181 | C2 | semidirect |
| 112. C181 | #3239 | semidirect |
| 122. #432 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153816 | 2 |
| #26041813 | 2 |
| #26041688 | 2 |
| #26041639 | 2 |
| #26041615 | 2 |
| #26041598 | 2 |
| #26041565 | 2 |
| #26041560 | 2 |
| #432×C181 | 2 |
| #3239 | 181 |