Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
174 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 49 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. C2×#22583555 | C2 | semidirect |
| 2. C2×#22583554 | C2 | semidirect |
| 4. #31826559 | C2 | semidirect |
| 5. Dic283⋊C16 | C2 | semidirect |
| 6. #31826265 | C2 | semidirect |
| 7. #357×C283 | C2 | semidirect |
| 26. Dic1132 | D4 | semidirect |
| 71. Dic283 | SD32 | semidirect |
| 77. C283 | #2207 | semidirect |
| 85. #357 | D283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22583555 | 2 |
| C2×#22583554 | 2 |
| #31826840 | 2 |
| #31826559 | 2 |
| Dic283⋊C16 | 2 |
| #31826265 | 2 |
| #357×C283 | 2 |
| #2207 | 283 |