Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
506 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 506 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 |
|---|---|---|
| 1. #20287721 | C2 | semidirect |
| 3. #20276943 | C2 | semidirect |
| 4. #20276858 | C2 | semidirect |
| 7. Q8×C16×C53 | C2 | semidirect |
| 72. Q8×C53 | SD32 | semidirect |
| 105. Q8×C16 | D53 | semidirect |
| 127. C53 | #33926 | semidirect |
| 179. Q8 | #13133162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287721 | 2 |
| Q8×D424 | 2 |
| #20276943 | 2 |
| #20276858 | 2 |
| #20276761 | 2 |
| C4×#13133162 | 2 |
| Q8×C16×C53 | 2 |
| #33926 | 53 |