Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
824 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#14582625 | C2 | semidirect |
| 3. #19132597 | C2 | direct (N × H) |
| 4. C2×C43×#343 | C2 | semidirect |
| 15. #14582625 | C22 | semidirect |
| 19. C43×#343 | C22 | semidirect |
| 195. C2×#343 | D43 | semidirect |
| 201. C2×C43 | #1345 | semidirect |
| 218. #343 | C2×D43 | semidirect |
| 221. C43 | C2×#1345 | semidirect |
| 399. C2 | #19132597 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14582816 | 2 |
| C2×#14582625 | 2 |
| #19132597 | 2 |
| C2×C43×#343 | 2 |
| C2×#1345 | 43 |