Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
362 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#21439892 | C2 | semidirect |
| 5. #29504670 | C2 | semidirect |
| 6. #29504535 | C2 | semidirect |
| 7. #336×C239 | C2 | semidirect |
| 19. #21439882 | C4 | semidirect |
| 41. C4⋊Dic239 | C2×C4 | semidirect |
| 53. C2×C8×C239 | C2×C4 | semidirect |
| 66. D956 | C4⋊C4 | semidirect |
| 123. C239 | #1864 | semidirect |
| 131. #336 | D239 | semidirect |
| 169. C2×C8 | C4×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D956 | 2 |
| C2×#21439892 | 2 |
| C2×#21439882 | 2 |
| #29504670 | 2 |
| #29504535 | 2 |
| #336×C239 | 2 |
| #1864 | 239 |