Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 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. #31823839 | C2 | semidirect |
| 2. #31823658 | C2 | semidirect |
| 3. D4×#14555886 | C2 | semidirect |
| 4. #31823215 | C2 | semidirect |
| 5. #31823207 | C2 | semidirect |
| 6. #31823206 | C2 | semidirect |
| 7. #459×C281 | C2 | semidirect |
| 53. #14555886 | D8 | semidirect |
| 62. D4×C281 | D8 | semidirect |
| 92. C281 | #1667 | semidirect |
| 96. #459 | D281 | semidirect |
| 151. D4 | #17985123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31823839 | 2 |
| #31823658 | 2 |
| D4×#14555886 | 2 |
| #31823215 | 2 |
| #31823207 | 2 |
| #31823206 | 2 |
| #459×C281 | 2 |
| #1667 | 281 |