Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×#13063269 | C2 | semidirect |
| 2. C2×#14583174 | C2 | semidirect |
| 3. C2×#14582712 | C2 | semidirect |
| 4. #19136314 | C2 | semidirect |
| 5. C2×#14582683 | C2 | semidirect |
| 6. #19132690 | C2 | semidirect |
| 37. C2×Dic172 | D4 | semidirect |
| 47. C2×C43⋊C16 | D4 | semidirect |
| 49. #13063261 | D4 | semidirect |
| 223. C43 | #13321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13063269 | 2 |
| C2×#14583174 | 2 |
| C2×#14582712 | 2 |
| #19136314 | 2 |
| C2×#14582683 | 2 |
| #19132690 | 2 |
| C43×#3058 | 2 |
| #13321 | 43 |