Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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. #19147731 | C2 | semidirect |
| 2. #19144316 | C2 | semidirect |
| 3. #19144258 | C2 | semidirect |
| 4. C2×#14582708 | C2 | semidirect |
| 5. #19136322 | C2 | semidirect |
| 6. #19136222 | C2 | semidirect |
| 7. C43×#1383 | C2 | semidirect |
| 50. C2×Dic172 | D4 | semidirect |
| 54. C2×D344 | D4 | semidirect |
| 83. C2×C16×C43 | D4 | semidirect |
| 85. #108×C43 | D4 | semidirect |
| 226. #1383 | D43 | semidirect |
| 259. C43 | #13318 | semidirect |
| 306. C2×C16 | D172 | semidirect |
| 308. #108 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147731 | 2 |
| #19144316 | 2 |
| #19144258 | 2 |
| C2×#14582708 | 2 |
| #19136322 | 2 |
| #19136222 | 2 |
| C43×#1383 | 2 |
| #13318 | 43 |