Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
520 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 152 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. (C2×#10624382)⋊Q8 | C2 | semidirect |
| 2. #26042229 | C2 | semidirect |
| 4. #26042226 | C2 | semidirect |
| 5. #26042223 | C2 | semidirect |
| 19. #19153805 | C4 | semidirect |
| 20. #19153804 | C4 | semidirect |
| 21. #19153803 | C4 | semidirect |
| 22. #19153802 | C4 | semidirect |
| 25. #124×C181 | C4 | semidirect |
| 37. C2×Dic362 | C2×C4 | semidirect |
| 38. C2×Dic362 | C2×C4 | semidirect |
| 48. C22⋊Dic181 | C2×C4 | semidirect |
| 49. #15668426 | C2×C4 | semidirect |
| 50. #15668426 | C2×C4 | semidirect |
| 51. C4×Dic181 | C2×C4 | semidirect |
| 52. C4×Dic181 | C2×C4 | semidirect |
| 53. C2×Q8×C181 | C2×C4 | semidirect |
| 55. C22⋊C4×C181 | C2×C4 | semidirect |
| 56. C42×C181 | C2×C4 | semidirect |
| 116. C181 | #2379 | semidirect |
| 131. #124 | #10624382 | semidirect |
| 148. C2×Q8 | C2×#10624382 | semidirect |
| 169. C22⋊C4 | C2×#10624382 | semidirect |
| 173. C42 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#10624382)⋊Q8 | 2 |
| #26042229 | 2 |
| #26042227 | 2 |
| #26042226 | 2 |
| #26042223 | 2 |
| #124×D181 | 2 |
| #2379 | 181 |