Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 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. #26042008 | C2 | semidirect |
| 4. #26041630 | C2 | semidirect |
| 5. #26041589 | C2 | semidirect |
| 8. #26041489 | C2 | semidirect |
| 9. C8×Dic362 | C2 | semidirect |
| 10. #26041371 | C2 | semidirect |
| 115. C181 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042008 | 2 |
| #26041999 | 2 |
| #26041632 | 2 |
| #26041630 | 2 |
| #26041589 | 2 |
| #26041559 | 2 |
| #26041499 | 2 |
| #26041489 | 2 |
| C8×Dic362 | 2 |
| #26041371 | 2 |
| C4×SD16×C181 | 2 |
| #3364 | 181 |