Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
236 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 236 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. #29505479 | C2 | semidirect |
| 2. #29505145 | C2 | semidirect |
| 3. #29504973 | C2 | semidirect |
| 5. #29504520 | C2 | semidirect |
| 6. #29504504 | C2 | semidirect |
| 7. D4⋊C8×C239 | C2 | semidirect |
| 66. D4×C239 | SD16 | semidirect |
| 96. C239 | #1622 | semidirect |
| 104. D4⋊C8 | D239 | semidirect |
| 158. D4 | #16838537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29505479 | 2 |
| #29505145 | 2 |
| #29504973 | 2 |
| #29504967 | 2 |
| #29504520 | 2 |
| #29504504 | 2 |
| D4⋊C8×C239 | 2 |
| #1622 | 239 |