Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
246 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 70 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. #20290313 | C2 | semidirect |
| 2. #20290311 | C2 | semidirect |
| 3. #20289741 | C2 | semidirect |
| 4. #20289674 | C2 | semidirect |
| 5. #20289673 | C2 | semidirect |
| 6. #20289632 | C2 | semidirect |
| 35. #13133158 | C8 | semidirect |
| 55. D8×C53 | C2×C8 | semidirect |
| 64. D424 | C2×C8 | semidirect |
| 67. #11719908 | C2×C8 | semidirect |
| 131. C53 | #12067 | semidirect |
| 160. D8 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290313 | 2 |
| #20290311 | 2 |
| #20289741 | 2 |
| #20289674 | 2 |
| #20289673 | 2 |
| #20289632 | 2 |
| #20276588 | 2 |
| #12067 | 53 |