Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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. D4×Dic566 | C2 | semidirect |
| 2. #31826812 | C2 | semidirect |
| 3. #31826666 | C2 | semidirect |
| 5. #31826212 | C2 | semidirect |
| 6. #31826197 | C2 | semidirect |
| 7. D4⋊C8×C283 | C2 | semidirect |
| 56. Dic566 | D8 | semidirect |
| 69. D4×C283 | SD16 | semidirect |
| 99. C283 | #1627 | semidirect |
| 107. D4⋊C8 | D283 | semidirect |
| 164. D4 | #17985381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic566 | 2 |
| #31826812 | 2 |
| #31826666 | 2 |
| #31826660 | 2 |
| #31826212 | 2 |
| #31826197 | 2 |
| D4⋊C8×C283 | 2 |
| #1627 | 283 |