Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
388 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. C2×#21439870 | C2 | semidirect |
| 5. C4⋊C4×Dic239 | C2 | semidirect |
| 6. #29504534 | C2 | semidirect |
| 7. #340×C239 | C2 | semidirect |
| 12. #21439922 | C4 | semidirect |
| 17. #21439882 | C4 | semidirect |
| 18. #21439880 | C4 | semidirect |
| 39. C2×C239⋊C8 | C2×C4 | semidirect |
| 41. C4⋊Dic239 | C2×C4 | semidirect |
| 51. C2×C8×C239 | C2×C4 | semidirect |
| 55. C4⋊C4×C239 | C2×C4 | semidirect |
| 66. D956 | C42 | semidirect |
| 123. C239 | #1762 | semidirect |
| 131. #340 | D239 | semidirect |
| 169. C2×C8 | C4×D239 | semidirect |
| 175. C4⋊C4 | C4×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439922 | 2 |
| C2×#21439882 | 2 |
| C2×#21439880 | 2 |
| C2×#21439870 | 2 |
| C4⋊C4×Dic239 | 2 |
| #29504534 | 2 |
| #340×C239 | 2 |
| #1762 | 239 |