Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
336 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 59 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. D4×D956 | C2 | semidirect |
| 2. #29505149 | C2 | semidirect |
| 3. #29504968 | C2 | semidirect |
| 4. #29504967 | C2 | semidirect |
| 5. #29504515 | C2 | semidirect |
| 6. #29504501 | C2 | semidirect |
| 7. D4⋊C8×C239 | C2 | semidirect |
| 14. #21439957 | C22 | semidirect |
| 19. C4⋊(C239⋊C8) | C22 | semidirect |
| 23. C4⋊C8×C239 | C22 | semidirect |
| 24. C4×C8×C239 | C22 | semidirect |
| 72. D956 | D8 | semidirect |
| 80. D4×C239 | D8 | semidirect |
| 117. C239 | #1619 | semidirect |
| 125. D4⋊C8 | D239 | semidirect |
| 139. C4⋊C8 | C2×D239 | semidirect |
| 142. C4×C8 | C2×D239 | semidirect |
| 194. D4 | D1912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D956 | 2 |
| #29505149 | 2 |
| #29504968 | 2 |
| #29504967 | 2 |
| #29504515 | 2 |
| #29504501 | 2 |
| D4⋊C8×C239 | 2 |
| #1619 | 239 |