Finite Group DatabasebetaFinite Group DatabasebetaOrder 35968.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #31824261 | C2 | semidirect |
| 2. C2×#22582904 | C2 | semidirect |
| 3. #31824032 | C2 | semidirect |
| 4. #31823481 | C2 | semidirect |
| 5. #31823467 | C2 | semidirect |
| 6. #31823233 | C2 | semidirect |
| 7. #410×C281 | C2 | semidirect |
| 56. #17985122 | D4 | semidirect |
| 58. C2×#14555886 | D4 | semidirect |
| 64. C2×Q8×C281 | D4 | semidirect |
| 66. C2×D4×C281 | D4 | semidirect |
| 142. C281 | #2008 | semidirect |
| 149. #410 | D281 | semidirect |
| 184. C2×Q8 | D1124 | semidirect |
| 195. C2×D4 | D1124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31824261 | 2 |
| C2×#22582904 | 2 |
| #31824032 | 2 |
| #31823481 | 2 |
| #31823467 | 2 |
| #31823233 | 2 |
| #410×C281 | 2 |
| #2008 | 281 |