Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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. #19133965 | C2 | semidirect |
| 4. #19132669 | C2 | semidirect |
| 5. #19132645 | C2 | semidirect |
| 7. Q8×C16×C43 | C2 | semidirect |
| 70. C16×C43 | SD16 | semidirect |
| 73. Q8×C43 | SD32 | semidirect |
| 107. Q8×C16 | D43 | semidirect |
| 132. C43 | #12441 | semidirect |
| 180. C16 | #10621884 | semidirect |
| 185. Q8 | #13063270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19136851 | 2 |
| #19133965 | 2 |
| #19133955 | 2 |
| #19132669 | 2 |
| #19132645 | 2 |
| #19132642 | 2 |
| Q8×C16×C43 | 2 |
| #12441 | 43 |