Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20287849 | C2 | semidirect |
| 2. #20284296 | C2 | semidirect |
| 3. #20276451 | C2 | semidirect |
| 4. #20276450 | C2 | semidirect |
| 5. #20276326 | C2 | semidirect |
| 6. #20272816 | C2 | semidirect |
| 7. C53×#3050 | C2 | semidirect |
| 38. C2×Dic212 | D4 | semidirect |
| 40. C2×D424 | D4 | semidirect |
| 56. C2×#11719908 | D4 | semidirect |
| 58. #13133149 | D4 | semidirect |
| 67. C2×Q16×C53 | D4 | semidirect |
| 69. C2×D8×C53 | D4 | semidirect |
| 85. #106×C53 | D4 | semidirect |
| 228. #3050 | D53 | semidirect |
| 265. C53 | #13309 | semidirect |
| 278. C2×Q16 | C22⋊D53 | semidirect |
| 282. C2×D8 | C22⋊D53 | semidirect |
| 316. #106 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| #20284296 | 2 |
| #20276451 | 2 |
| #20276450 | 2 |
| #20276326 | 2 |
| #20272816 | 2 |
| C53×#3050 | 2 |
| #13309 | 53 |