Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
568 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20284297 | C2 | semidirect |
| 3. #20284292 | C2 | semidirect |
| 4. #20276452 | C2 | semidirect |
| 5. #20276325 | C2 | semidirect |
| 6. #20272816 | C2 | semidirect |
| 7. C53×#2145 | C2 | semidirect |
| 39. C2×Dic212 | D4 | semidirect |
| 41. C2×D424 | D4 | semidirect |
| 66. C2×#11719908 | D4 | semidirect |
| 68. #13133149 | D4 | semidirect |
| 78. C2×Q16×C53 | D4 | semidirect |
| 80. C2×D8×C53 | D4 | semidirect |
| 87. #106×C53 | D4 | semidirect |
| 230. #2145 | D53 | semidirect |
| 265. C53 | #13309 | semidirect |
| 278. C2×Q16 | D212 | semidirect |
| 282. C2×D8 | D212 | 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 |
| #20284297 | 2 |
| #20284292 | 2 |
| #20276452 | 2 |
| #20276325 | 2 |
| #20272816 | 2 |
| C53×#2145 | 2 |
| #13309 | 53 |