Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 346 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. #26042346 | C2 | semidirect |
| 2. #26042278 | C2 | semidirect |
| 3. #26042271 | C2 | semidirect |
| 4. #26042260 | C2 | semidirect |
| 5. #26042161 | C2 | semidirect |
| 6. #26042147 | C2 | semidirect |
| 22. C2×#15668436 | C4 | semidirect |
| 23. C2×D1448 | C4 | semidirect |
| 24. C2×#15668434 | C4 | semidirect |
| 26. C2×SD16×C181 | C4 | semidirect |
| 48. C2×D724 | C2×C4 | semidirect |
| 61. C2×#13089678 | C2×C4 | semidirect |
| 62. C2×Q8×C181 | C2×C4 | semidirect |
| 65. C2×C8×C181 | C2×C4 | semidirect |
| 128. C181 | #1904 | semidirect |
| 142. C2×SD16 | #10624382 | semidirect |
| 161. C2×Q8 | C2×#10624382 | semidirect |
| 184. C2×C8 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042346 | 2 |
| #26042278 | 2 |
| #26042271 | 2 |
| #26042260 | 2 |
| #26042161 | 2 |
| #26042147 | 2 |
| C2×#19153843 | 2 |
| #1904 | 181 |