Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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. #29504672 | C2 | semidirect |
| 3. #29504664 | C2 | semidirect |
| 4. #29504655 | C2 | semidirect |
| 5. #29504650 | C2 | semidirect |
| 6. #29504648 | C2 | semidirect |
| 7. #29504646 | C2 | semidirect |
| 8. #29504632 | C2 | semidirect |
| 9. #381×C239 | C2 | semidirect |
| 13. #21439934 | C4 | semidirect |
| 37. C2×C22⋊D239 | C2×C4 | semidirect |
| 45. C4⋊Dic239 | C2×C4 | semidirect |
| 52. (C2×D239)⋊C4 | C2×C4 | semidirect |
| 56. C22×C4×C239 | C2×C4 | semidirect |
| 129. C239 | #2377 | semidirect |
| 138. #381 | D239 | semidirect |
| 176. C22×C4 | C4×D239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21439934 | 2 |
| #29504672 | 2 |
| #29504664 | 2 |
| #29504655 | 2 |
| #29504650 | 2 |
| #29504648 | 2 |
| #29504646 | 2 |
| #29504632 | 2 |
| #381×C239 | 2 |
| #2377 | 239 |