Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1060 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 1060 conjugacy classes of subgroups — too many to draw. Only its 105 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×#16810756 | C2 | semidirect |
| 2. #20278353 | C2 | semidirect |
| 3. #20275552 | C2 | semidirect |
| 4. #20274647 | C2 | semidirect |
| 5. #20273283 | C2 | semidirect |
| 6. #20272562 | C2 | semidirect |
| 7. C53×#3186 | C2 | semidirect |
| 55. C22⋊#88322 | D4 | semidirect |
| 61. C22×D4×C53 | D4 | semidirect |
| 64. C22×C8×C53 | D4 | semidirect |
| 74. C2×C4⋊C4×C53 | D4 | semidirect |
| 146. C22⋊Dic53 | D8 | semidirect |
| 259. #3186 | D53 | semidirect |
| 299. C53 | #9946 | semidirect |
| 312. C22×D4 | C22⋊D53 | semidirect |
| 318. C22×C8 | C22⋊D53 | semidirect |
| 332. C2×C4⋊C4 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810756 | 2 |
| #20278353 | 2 |
| #20275552 | 2 |
| #20274647 | 2 |
| #20273283 | 2 |
| #20272562 | 2 |
| C53×#3186 | 2 |
| #9946 | 53 |