Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31827200 | C2 | semidirect |
| 2. #31826850 | C2 | semidirect |
| 4. #31826683 | C2 | semidirect |
| 5. #31826665 | C2 | semidirect |
| 6. C8×Dic566 | C2 | semidirect |
| 7. #31826547 | C2 | semidirect |
| 8. C4×Q16×C283 | C2 | semidirect |
| 86. C283 | #3396 | semidirect |
| 94. C4×Q16 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827200 | 2 |
| #31826850 | 2 |
| #31826842 | 2 |
| #31826683 | 2 |
| #31826665 | 2 |
| C8×Dic566 | 2 |
| #31826547 | 2 |
| C4×Q16×C283 | 2 |
| #3396 | 283 |