Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
284 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26041317 | C2 | semidirect |
| 2. #26041296 | C2 | semidirect |
| 3. #26041253 | C2 | semidirect |
| 4. #26041234 | C2 | semidirect |
| 20. C2×Q16×C181 | C4 | semidirect |
| 21. C2×SD16×C181 | C4 | semidirect |
| 22. C2×D8×C181 | C4 | semidirect |
| 96. C181 | #1976 | semidirect |
| 108. C2×Q16 | Dic181 | semidirect |
| 109. C2×SD16 | Dic181 | semidirect |
| 110. C2×D8 | Dic181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041317 | 2 |
| #26041296 | 2 |
| #26041253 | 2 |
| #26041234 | 2 |
| C2×#135×C181 | 2 |
| #1976 | 181 |