Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 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×C22⋊C4×D239 | C2 | semidirect |
| 3. C2×#21439874 | C2 | semidirect |
| 4. C2×#21439874 | C2 | semidirect |
| 5. #29504627 | C2 | semidirect |
| 6. #29504539 | C2 | semidirect |
| 7. #342×C239 | C2 | semidirect |
| 9. C22×D956 | C4 | semidirect |
| 19. C2×(C2×D239)⋊C4 | C4 | semidirect |
| 33. C23×D239 | C2×C4 | semidirect |
| 48. C22×Dic239 | C2×C4 | semidirect |
| 54. C22⋊Dic239 | D4 | semidirect |
| 62. C22×C4×C239 | C2×C4 | semidirect |
| 68. C22⋊C4×C239 | D4 | semidirect |
| 152. C2×D239 | #99 | semidirect |
| 170. C239 | #1898 | semidirect |
| 178. #342 | D239 | semidirect |
| 225. C22×C4 | C4×D239 | semidirect |
| 239. C22⋊C4 | D956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439930 | 2 |
| C2×C22⋊C4×D239 | 2 |
| C2×#21439874 | 2 |
| #29504627 | 2 |
| #29504539 | 2 |
| #342×C239 | 2 |
| #1898 | 239 |