Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 2. #29505170 | C2 | semidirect |
| 3. #29505057 | C2 | semidirect |
| 5. #29504517 | C2 | semidirect |
| 7. Q8⋊C8×C239 | C2 | semidirect |
| 66. Q8×C239 | SD16 | semidirect |
| 92. C239 | #1651 | semidirect |
| 99. Q8⋊C8 | D239 | semidirect |
| 150. Q8 | #16838537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D956 | 2 |
| #29505170 | 2 |
| #29505057 | 2 |
| #29504978 | 2 |
| #29504517 | 2 |
| #29504501 | 2 |
| Q8⋊C8×C239 | 2 |
| #1651 | 239 |