Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
648 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#16811015 | C2 | semidirect |
| 2. C2×#16810985 | C2 | semidirect |
| 4. C2×#16810362 | C2 | semidirect |
| 5. C2×#16810362 | C2 | semidirect |
| 6. #20272596 | C2 | semidirect |
| 7. C53×#1993 | C2 | semidirect |
| 60. #13133128 | D4 | semidirect |
| 61. #13133128 | D4 | semidirect |
| 68. C4⋊Q8×C53 | D4 | semidirect |
| 207. #1993 | D53 | semidirect |
| 241. C53 | #10081 | semidirect |
| 258. C4⋊Q8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811015 | 2 |
| C2×#16810985 | 2 |
| #20282761 | 2 |
| C2×#16810362 | 2 |
| #20272596 | 2 |
| C53×#1993 | 2 |
| #10081 | 53 |