Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
174 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 79 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×C16×D239 | C2 | semidirect |
| 3. (C2×D239)⋊C16 | C2 | semidirect |
| 4. C4×C239⋊C16 | C2 | semidirect |
| 5. C4⋊C16×C239 | C2 | semidirect |
| 23. C239⋊C16 | D4 | semidirect |
| 29. D956 | C16 | semidirect |
| 43. C2×D239 | C2×C16 | semidirect |
| 45. C4×C239 | C2×C16 | semidirect |
| 53. C239 | D4×C16 | semidirect |
| 57. C4⋊C16 | D239 | semidirect |
| 100. C4 | C16×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×D239 | 2 |
| C8×D956 | 2 |
| (C2×D239)⋊C16 | 2 |
| C4×C239⋊C16 | 2 |
| C4⋊C16×C239 | 2 |
| D4×C16 | 239 |