Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #29505570 | C2 | semidirect |
| 2. C2×#21439988 | C2 | semidirect |
| 3. #29505336 | C2 | semidirect |
| 4. #29504776 | C2 | semidirect |
| 5. #29504745 | C2 | semidirect |
| 6. #29504544 | C2 | semidirect |
| 7. #421×C239 | C2 | semidirect |
| 36. C2×Dic478 | D4 | semidirect |
| 43. C2×D956 | D4 | semidirect |
| 55. C2×C239⋊C8 | D4 | semidirect |
| 70. M16×C239 | D4 | semidirect |
| 142. C239 | #2008 | semidirect |
| 147. #421 | D239 | semidirect |
| 208. M16 | C22⋊D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29505570 | 2 |
| C2×#21439988 | 2 |
| #29505336 | 2 |
| #29504776 | 2 |
| #29504745 | 2 |
| #29504544 | 2 |
| #421×C239 | 2 |
| #2008 | 239 |