Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. #19136397 | C2 | semidirect |
| 3. C4×#13063264 | C2 | semidirect |
| 4. Q8⋊(C43⋊C16) | C2 | semidirect |
| 5. #19132551 | C2 | semidirect |
| 6. #19132549 | C2 | semidirect |
| 7. C43×Q8⋊C16 | C2 | semidirect |
| 105. Q8×C43 | M32 | semidirect |
| 117. D172 | M32 | semidirect |
| 157. Q8⋊C16 | D43 | semidirect |
| 184. C43 | #11615 | semidirect |
| 263. Q8 | #13063264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#10621902 | 2 |
| #19136397 | 2 |
| C4×#13063264 | 2 |
| Q8⋊(C43⋊C16) | 2 |
| #19132551 | 2 |
| #19132549 | 2 |
| C43×Q8⋊C16 | 2 |
| #11615 | 43 |