Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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. #31800398 | C2 | semidirect |
| 2. #31800287 | C2 | semidirect |
| 4. #31799748 | C2 | semidirect |
| 5. Q8⋊#14555660 | C2 | semidirect |
| 61. Q8×C277 | SD16 | semidirect |
| 92. C277 | #1651 | semidirect |
| 150. Q8 | #17984551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800398 | 2 |
| #31800287 | 2 |
| #31800207 | 2 |
| #31799748 | 2 |
| Q8⋊#14555660 | 2 |
| D4⋊#14555660 | 2 |
| D4×Q8×C277 | 2 |
| #1651 | 277 |