Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
548 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 548 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. C2×#14582946 | C2 | semidirect |
| 3. C2×#14582712 | C2 | semidirect |
| 4. C2×#14582680 | C2 | semidirect |
| 5. #19132695 | C2 | semidirect |
| 6. #19132694 | C2 | semidirect |
| 7. C2×C43×#361 | C2 | semidirect |
| 48. #13063261 | D4 | semidirect |
| 66. #108×C43 | D4 | semidirect |
| 176. C2×#361 | D43 | semidirect |
| 204. C43 | #13010 | semidirect |
| 242. #108 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583149 | 2 |
| C2×#14582946 | 2 |
| C2×#14582712 | 2 |
| C2×#14582680 | 2 |
| #19132695 | 2 |
| #19132694 | 2 |
| C2×C43×#361 | 2 |
| #13010 | 43 |