Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
176 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 53 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. #31826812 | C2 | semidirect |
| 2. #31826756 | C2 | semidirect |
| 4. C8×D1132 | C2 | semidirect |
| 5. #31826213 | C2 | semidirect |
| 6. #31826208 | C2 | semidirect |
| 7. #334×C283 | C2 | semidirect |
| 82. C283 | #1677 | semidirect |
| 88. #334 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31826812 | 2 |
| #31826756 | 2 |
| #31826661 | 2 |
| C8×D1132 | 2 |
| #31826213 | 2 |
| #31826208 | 2 |
| #334×C283 | 2 |
| #1677 | 283 |