Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26041652 | C2 | semidirect |
| 2. #26041560 | C2 | semidirect |
| 4. C8×D724 | C2 | semidirect |
| 5. #26041024 | C2 | semidirect |
| 6. #26041022 | C2 | semidirect |
| 7. #334×C181 | C2 | semidirect |
| 53. D724 | SD16 | semidirect |
| 65. C8×C181 | D8 | semidirect |
| 85. C181 | #1665 | semidirect |
| 91. #334 | D181 | semidirect |
| 151. C8 | D1448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041652 | 2 |
| #26041560 | 2 |
| #26041475 | 2 |
| C8×D724 | 2 |
| #26041024 | 2 |
| #26041022 | 2 |
| #334×C181 | 2 |
| #1665 | 181 |