Finite Group DatabasebetaFinite Group DatabasebetaOrder 35456.
168 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 168 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. #31800132 | C2 | semidirect |
| 3. #31799752 | C2 | semidirect |
| 4. #31799732 | C2 | semidirect |
| 6. #31799723 | C2 | semidirect |
| 60. C8×C277 | SD16 | semidirect |
| 77. C277 | #1582 | semidirect |
| 138. C8 | #17984551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31800132 | 2 |
| C4×#17984551 | 2 |
| #31799752 | 2 |
| #31799732 | 2 |
| D4⋊#14555660 | 2 |
| #31799723 | 2 |
| C8×D4×C277 | 2 |
| #1582 | 277 |