Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
338 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 73 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. Q8×D344 | C2 | semidirect |
| 2. #19136819 | C2 | semidirect |
| 4. #19133955 | C2 | semidirect |
| 5. #19132649 | C2 | semidirect |
| 6. #19132557 | C2 | semidirect |
| 7. C43×Q8⋊C16 | C2 | semidirect |
| 83. D344 | SD16 | semidirect |
| 89. Q8×C43 | D16 | semidirect |
| 137. Q8⋊C16 | D43 | semidirect |
| 161. C43 | #12352 | semidirect |
| 229. Q8 | D688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D344 | 2 |
| #19136819 | 2 |
| #19136631 | 2 |
| #19133955 | 2 |
| #19132649 | 2 |
| #19132557 | 2 |
| C43×Q8⋊C16 | 2 |
| #12352 | 43 |