Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
232 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 232 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. C2×#14582734 | C2 | semidirect |
| 2. C4×D688 | C2 | semidirect |
| 3. C4⋊(C43⋊C32) | C2 | semidirect |
| 4. #19132773 | C2 | semidirect |
| 5. C43×#2246 | C2 | semidirect |
| 19. D688 | D4 | semidirect |
| 75. C4×C43 | D32 | semidirect |
| 80. #2246 | D43 | semidirect |
| 99. C43 | #13685 | semidirect |
| 159. C4 | #14582734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582734 | 2 |
| C4×D688 | 2 |
| C4⋊(C43⋊C32) | 2 |
| #19132773 | 2 |
| C43×#2246 | 2 |
| #13685 | 43 |