Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
482 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. #20290268 | C2 | semidirect |
| 4. #20290266 | C2 | semidirect |
| 5. #20289548 | C2 | semidirect |
| 6. #20289548 | C2 | semidirect |
| 59. #13133133 | C8 | semidirect |
| 96. M16×C53 | C2×C8 | semidirect |
| 110. #11719917 | C2×C8 | semidirect |
| 206. C53 | #8835 | semidirect |
| 267. M16 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291565 | 2 |
| #20290837 | 2 |
| #20290268 | 2 |
| #20290266 | 2 |
| #20289548 | 2 |
| #20274506 | 2 |
| #8835 | 53 |