Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
696 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 143 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. C2×#14583328 | C2 | semidirect |
| 2. #19146353 | C2 | semidirect |
| 3. #19136678 | C2 | semidirect |
| 4. #19136632 | C2 | semidirect |
| 5. #19136515 | C2 | semidirect |
| 6. C4×Dic344 | C2 | semidirect |
| 7. C16×D172 | C2 | semidirect |
| 8. C43×#2246 | C2 | semidirect |
| 41. Dic344 | D4 | semidirect |
| 123. C4×C43 | #508 | semidirect |
| 131. #2246 | D43 | semidirect |
| 162. C43 | #33853 | semidirect |
| 259. C4 | #14583328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583328 | 2 |
| #19146353 | 2 |
| #19136678 | 2 |
| #19136632 | 2 |
| #19136515 | 2 |
| C4×Dic344 | 2 |
| C16×D172 | 2 |
| C43×#2246 | 2 |
| #33853 | 43 |