Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#14583337 | C2 | semidirect |
| 3. #19145081 | C2 | semidirect |
| 4. #19136332 | C2 | semidirect |
| 5. #19136312 | C2 | semidirect |
| 6. #19135493 | C2 | semidirect |
| 7. C43×#1378 | C2 | semidirect |
| 47. C2×Dic172 | D4 | semidirect |
| 59. C2×D344 | D4 | semidirect |
| 81. M32×C43 | D4 | semidirect |
| 83. C2×C16×C43 | D4 | semidirect |
| 217. #1378 | D43 | semidirect |
| 250. C43 | #13334 | semidirect |
| 295. M32 | D172 | semidirect |
| 297. C2×C16 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147731 | 2 |
| C2×#14583337 | 2 |
| #19145081 | 2 |
| #19136332 | 2 |
| #19136312 | 2 |
| #19135493 | 2 |
| C43×#1378 | 2 |
| #13334 | 43 |