Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. #31827137 | C2 | semidirect |
| 2. Q8×D1132 | C2 | semidirect |
| 3. #31826812 | C2 | semidirect |
| 4. #31826746 | C2 | semidirect |
| 5. #31826661 | C2 | semidirect |
| 6. C4×D2264 | C2 | semidirect |
| 7. C8×Q8×C283 | C2 | semidirect |
| 52. D1132 | #41 | semidirect |
| 57. Q8×C283 | D8 | semidirect |
| 81. C283 | #3358 | semidirect |
| 88. C8×Q8 | D283 | semidirect |
| 129. Q8 | D2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827137 | 2 |
| Q8×D1132 | 2 |
| #31826812 | 2 |
| #31826746 | 2 |
| #31826661 | 2 |
| C4×D2264 | 2 |
| C8×Q8×C283 | 2 |
| #3358 | 283 |