Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
458 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 73 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. D4×D344 | C2 | semidirect |
| 2. #19136844 | C2 | semidirect |
| 3. #19136627 | C2 | semidirect |
| 4. #19132640 | C2 | semidirect |
| 5. #19132555 | C2 | semidirect |
| 6. D4⋊(C43⋊C16) | C2 | semidirect |
| 7. C43×#1667 | C2 | semidirect |
| 17. C4⋊(C43⋊C16) | C22 | semidirect |
| 19. C4×C43⋊C16 | C22 | semidirect |
| 20. C43×#493 | C22 | semidirect |
| 23. C43×#335 | C22 | semidirect |
| 94. D344 | D8 | semidirect |
| 110. D4×C43 | D16 | semidirect |
| 159. #1667 | D43 | semidirect |
| 175. #493 | C2×D43 | semidirect |
| 185. #335 | C2×D43 | semidirect |
| 187. C43 | #12316 | semidirect |
| 282. D4 | #13063266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D344 | 2 |
| #19136844 | 2 |
| #19136627 | 2 |
| #19132640 | 2 |
| #19132555 | 2 |
| D4⋊(C43⋊C16) | 2 |
| C43×#1667 | 2 |
| #12316 | 43 |