Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31826815 | C2 | semidirect |
| 3. #31826793 | C2 | semidirect |
| 4. #31826750 | C2 | semidirect |
| 5. #31826696 | C2 | semidirect |
| 6. #31826667 | C2 | semidirect |
| 7. #31826604 | C2 | semidirect |
| 8. C4×#17985379 | C2 | semidirect |
| 9. D4×C283⋊C8 | C2 | semidirect |
| 10. C2×#22583534 | C2 | semidirect |
| 11. D4×Q8×C283 | C2 | semidirect |
| 94. Q8×C283 | #41 | semidirect |
| 95. D4×C283 | SD16 | semidirect |
| 128. C283 | #3298 | semidirect |
| 130. D4×Q8 | D283 | semidirect |
| 213. Q8 | #17985391 | semidirect |
| 217. D4 | #17985379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827119 | 2 |
| #31826815 | 2 |
| #31826793 | 2 |
| #31826750 | 2 |
| #31826696 | 2 |
| #31826667 | 2 |
| #31826604 | 2 |
| C4×#17985379 | 2 |
| D4×C283⋊C8 | 2 |
| C2×#22583534 | 2 |
| D4×Q8×C283 | 2 |
| #3298 | 283 |