Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
572 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 117 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×#106×D43 | C2 | semidirect |
| 3. C2×#14582709 | C2 | semidirect |
| 4. #19136205 | C2 | semidirect |
| 5. #19132702 | C2 | semidirect |
| 6. #19132701 | C2 | semidirect |
| 7. C2×C43×#360 | C2 | semidirect |
| 12. #14583137 | C4 | semidirect |
| 13. #14583132 | C4 | semidirect |
| 49. #13063259 | C2×C4 | semidirect |
| 52. #13063257 | D4 | semidirect |
| 61. C2×Q16×C43 | C2×C4 | semidirect |
| 63. C2×D8×C43 | C2×C4 | semidirect |
| 70. #106×C43 | D4 | semidirect |
| 176. C2×D43 | #360 | semidirect |
| 189. C2×#360 | D43 | semidirect |
| 218. C43 | #13001 | semidirect |
| 226. C2×Q16 | C4×D43 | semidirect |
| 228. C2×D8 | C4×D43 | semidirect |
| 260. #106 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144172 | 2 |
| C2×#106×D43 | 2 |
| C2×#14582709 | 2 |
| #19136205 | 2 |
| #19132702 | 2 |
| #19132701 | 2 |
| C2×C43×#360 | 2 |
| #13001 | 43 |