Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26041859 | C2 | semidirect |
| 2. #26041608 | C2 | semidirect |
| 3. #26041599 | C2 | semidirect |
| 4. #26041532 | C2 | semidirect |
| 5. #26041510 | C2 | semidirect |
| 6. #26041440 | C2 | semidirect |
| 7. #26041427 | C2 | semidirect |
| 8. #26041247 | C2 | semidirect |
| 9. #470×C181 | C2 | semidirect |
| 117. C181 | #3204 | semidirect |
| 122. #470 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041859 | 2 |
| #26041608 | 2 |
| #26041599 | 2 |
| #26041532 | 2 |
| #26041510 | 2 |
| #26041440 | 2 |
| #26041427 | 2 |
| #26041247 | 2 |
| #470×C181 | 2 |
| #3204 | 181 |