Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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. #19145513 | C2 | semidirect |
| 2. #19144059 | C2 | semidirect |
| 3. #19133263 | C2 | semidirect |
| 4. #19133089 | C2 | semidirect |
| 5. #19132986 | C2 | semidirect |
| 6. #19132498 | C2 | semidirect |
| 7. C43×#2541 | C2 | semidirect |
| 38. #13063325 | D4 | semidirect |
| 39. #13063322 | D4 | semidirect |
| 47. C4⋊(C43⋊C8) | D4 | semidirect |
| 48. C4⋊(C43⋊C8) | D4 | semidirect |
| 102. C2×D4×C43 | D8 | semidirect |
| 235. #2541 | D43 | semidirect |
| 271. C43 | #10238 | semidirect |
| 352. C2×D4 | #10621882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145513 | 2 |
| #19144059 | 2 |
| #19133263 | 2 |
| #19133089 | 2 |
| #19132986 | 2 |
| #19132498 | 2 |
| C43×#2541 | 2 |
| #10238 | 43 |