Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
364 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 179 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. #31826595 | C2 | semidirect |
| 3. #31826592 | C2 | semidirect |
| 4. Q8×C283⋊C8 | C2 | semidirect |
| 7. C8×Q8×C283 | C2 | semidirect |
| 73. C283 | #2984 | semidirect |
| 79. C8×Q8 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D283 | 2 |
| #31826595 | 2 |
| #31826592 | 2 |
| Q8×C283⋊C8 | 2 |
| #31826521 | 2 |
| #31826516 | 2 |
| C8×Q8×C283 | 2 |
| #2984 | 283 |