Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #19143192 | C2 | semidirect |
| 3. #19136310 | C2 | semidirect |
| 4. C2×#14582701 | C2 | semidirect |
| 5. C2×#14582682 | C2 | semidirect |
| 6. #19132705 | C2 | semidirect |
| 7. C43×#1382 | C2 | semidirect |
| 14. #14583170 | C4 | semidirect |
| 39. C2×D344 | C2×C4 | semidirect |
| 68. #108×C43 | C2×C4 | semidirect |
| 188. #1382 | D43 | semidirect |
| 216. C43 | #12996 | semidirect |
| 252. #108 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583170 | 2 |
| #19143192 | 2 |
| #19136310 | 2 |
| C2×#14582701 | 2 |
| C2×#14582682 | 2 |
| #19132705 | 2 |
| C43×#1382 | 2 |
| #12996 | 43 |