Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
528 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 165 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. Q8×Dic172 | C2 | semidirect |
| 3. #19136819 | C2 | semidirect |
| 4. #19136743 | C2 | semidirect |
| 5. #19136636 | C2 | semidirect |
| 6. C4×#13063270 | C2 | semidirect |
| 7. Q8×C16×C43 | C2 | semidirect |
| 65. Dic172 | #41 | semidirect |
| 72. Q8×C43 | SD32 | semidirect |
| 107. Q8×C16 | D43 | semidirect |
| 129. C43 | #33929 | semidirect |
| 181. Q8 | #13063270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147570 | 2 |
| Q8×Dic172 | 2 |
| #19136819 | 2 |
| #19136743 | 2 |
| #19136636 | 2 |
| C4×#13063270 | 2 |
| Q8×C16×C43 | 2 |
| #33929 | 43 |