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 |
|---|---|---|
| 3. #19136315 | C2 | semidirect |
| 5. #19132701 | C2 | semidirect |
| 6. #19132700 | C2 | semidirect |
| 7. C43×#2141 | C2 | semidirect |
| 13. #14583154 | C4 | semidirect |
| 53. #13063257 | C2×C4 | semidirect |
| 62. C2×Q16×C43 | C2×C4 | semidirect |
| 176. #2141 | D43 | semidirect |
| 203. C43 | #13000 | semidirect |
| 211. C2×Q16 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583154 | 2 |
| #19143183 | 2 |
| #19136315 | 2 |
| C2×#14582680 | 2 |
| #19132701 | 2 |
| #19132700 | 2 |
| C43×#2141 | 2 |
| #13000 | 43 |