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. #26041561 | C2 | semidirect |
| 5. #26041490 | C2 | semidirect |
| 6. #26041489 | C2 | semidirect |
| 8. #26041385 | C2 | semidirect |
| 9. #26041383 | C2 | semidirect |
| 11. #475×C181 | C2 | semidirect |
| 132. C181 | #3113 | semidirect |
| 138. #475 | 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 |
| #26041611 | 2 |
| #26041561 | 2 |
| #26041490 | 2 |
| #26041489 | 2 |
| #26041436 | 2 |
| #26041385 | 2 |
| #26041383 | 2 |
| #26041335 | 2 |
| #475×C181 | 2 |
| #3113 | 181 |