Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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. #26042289 | C2 | semidirect |
| 2. #26042278 | C2 | semidirect |
| 3. #26042277 | C2 | semidirect |
| 4. #26042260 | C2 | semidirect |
| 5. #26042259 | C2 | semidirect |
| 6. #26042242 | C2 | semidirect |
| 26. C2×#15668439 | C4 | semidirect |
| 27. C2×#15668438 | C4 | semidirect |
| 28. C2×#15668434 | C4 | semidirect |
| 30. C2×SD16×C181 | C4 | semidirect |
| 132. C181 | #1976 | semidirect |
| 149. C2×SD16 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042289 | 2 |
| #26042278 | 2 |
| #26042277 | 2 |
| #26042260 | 2 |
| #26042259 | 2 |
| #26042242 | 2 |
| C2×#19153837 | 2 |
| #1976 | 181 |