Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26042015 | C2 | semidirect |
| 2. #26042014 | C2 | semidirect |
| 3. #26041660 | C2 | semidirect |
| 5. #26041496 | C2 | semidirect |
| 6. #26041493 | C2 | semidirect |
| 7. #26041480 | C2 | semidirect |
| 8. #26041403 | C2 | semidirect |
| 9. C4×#15668439 | C2 | semidirect |
| 10. #26041359 | C2 | semidirect |
| 11. #460×C181 | C2 | semidirect |
| 127. C181 | #3396 | semidirect |
| 136. #460 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042015 | 2 |
| #26042014 | 2 |
| #26041660 | 2 |
| #26041655 | 2 |
| #26041496 | 2 |
| #26041493 | 2 |
| #26041480 | 2 |
| #26041403 | 2 |
| C4×#15668439 | 2 |
| #26041359 | 2 |
| #460×C181 | 2 |
| #3396 | 181 |