Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #26041315 | C2 | semidirect |
| 3. #26041295 | C2 | semidirect |
| 4. #26041253 | C2 | semidirect |
| 5. #26041252 | C2 | semidirect |
| 6. #26041237 | C2 | semidirect |
| 7. #421×C181 | C2 | semidirect |
| 13. C2×#15668439 | C4 | semidirect |
| 14. C2×#15668437 | C4 | semidirect |
| 15. C2×#15668436 | C4 | semidirect |
| 16. C2×#15668434 | C4 | semidirect |
| 132. C181 | #1976 | semidirect |
| 137. #421 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153836 | 2 |
| #26041315 | 2 |
| #26041295 | 2 |
| #26041253 | 2 |
| #26041252 | 2 |
| #26041237 | 2 |
| #421×C181 | 2 |
| #1976 | 181 |