Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 4. #26041565 | C2 | semidirect |
| 5. #26041564 | C2 | semidirect |
| 6. #26041486 | C2 | semidirect |
| 8. #26041386 | C2 | semidirect |
| 9. #26041383 | C2 | semidirect |
| 11. #462×C181 | C2 | semidirect |
| 132. C181 | #3113 | semidirect |
| 140. #462 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| C4×Q8×D181 | 2 |
| #26041608 | 2 |
| #26041565 | 2 |
| #26041564 | 2 |
| #26041486 | 2 |
| #26041433 | 2 |
| #26041386 | 2 |
| #26041383 | 2 |
| #26041335 | 2 |
| #462×C181 | 2 |
| #3113 | 181 |