Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 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. #20287851 | C2 | semidirect |
| 2. #20284436 | C2 | semidirect |
| 3. #20284378 | C2 | semidirect |
| 4. C2×#16810432 | C2 | semidirect |
| 5. #20276442 | C2 | semidirect |
| 6. #20276342 | C2 | semidirect |
| 7. C53×#1383 | C2 | semidirect |
| 50. C2×Dic212 | D4 | semidirect |
| 54. C2×D424 | D4 | semidirect |
| 83. C2×C16×C53 | D4 | semidirect |
| 85. #108×C53 | D4 | semidirect |
| 226. #1383 | D53 | semidirect |
| 259. C53 | #13318 | semidirect |
| 306. C2×C16 | D212 | semidirect |
| 308. #108 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287851 | 2 |
| #20284436 | 2 |
| #20284378 | 2 |
| C2×#16810432 | 2 |
| #20276442 | 2 |
| #20276342 | 2 |
| C53×#1383 | 2 |
| #13318 | 53 |