Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #29505151 | C2 | semidirect |
| 4. #29504524 | C2 | semidirect |
| 5. #29504518 | C2 | semidirect |
| 6. #29504517 | C2 | semidirect |
| 53. D4×C239 | Q16 | semidirect |
| 78. C239 | #1669 | semidirect |
| 127. D4 | #16838538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29505151 | 2 |
| #29505052 | 2 |
| D4×C239⋊C8 | 2 |
| #29504524 | 2 |
| #29504518 | 2 |
| #29504517 | 2 |
| #474×C239 | 2 |
| #1669 | 239 |