Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 210 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. #29505501 | C2 | semidirect |
| 4. #29504517 | C2 | semidirect |
| 5. Q8⋊(C239⋊C8) | C2 | semidirect |
| 6. #29504502 | C2 | semidirect |
| 60. Q8×C239 | SD16 | semidirect |
| 90. C239 | #1626 | semidirect |
| 146. Q8 | #16838536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29505501 | 2 |
| #29505118 | 2 |
| #29504969 | 2 |
| #29504517 | 2 |
| Q8⋊(C239⋊C8) | 2 |
| #29504502 | 2 |
| #460×C239 | 2 |
| #1626 | 239 |