Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
458 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 71 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. D8×D172 | C2 | semidirect |
| 2. #19136845 | C2 | semidirect |
| 3. #19136630 | C2 | semidirect |
| 4. #19133951 | C2 | semidirect |
| 5. #19132640 | C2 | semidirect |
| 6. #19132551 | C2 | semidirect |
| 7. C43×#1331 | C2 | semidirect |
| 13. #14583276 | C22 | semidirect |
| 19. C4⋊(C43⋊C16) | C22 | semidirect |
| 23. C4×C16×C43 | C22 | semidirect |
| 24. C43×#335 | C22 | semidirect |
| 74. D8×C43 | D8 | semidirect |
| 126. D172 | D16 | semidirect |
| 161. #1331 | D43 | semidirect |
| 184. C4×C16 | C2×D43 | semidirect |
| 185. #335 | C2×D43 | semidirect |
| 187. C43 | #12316 | semidirect |
| 245. D8 | D344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×D172 | 2 |
| #19136845 | 2 |
| #19136630 | 2 |
| #19133951 | 2 |
| #19132640 | 2 |
| #19132551 | 2 |
| C43×#1331 | 2 |
| #12316 | 43 |