Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
662 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20285179 | C2 | semidirect |
| 2. #20284807 | C2 | semidirect |
| 3. #20280568 | C2 | semidirect |
| 4. #20273263 | C2 | semidirect |
| 5. #20273157 | C2 | semidirect |
| 6. #20272581 | C2 | semidirect |
| 7. C53×#1533 | C2 | semidirect |
| 45. #13133217 | D4 | semidirect |
| 46. #13133214 | D4 | semidirect |
| 64. C4×#88322 | D4 | semidirect |
| 83. #97×C53 | D4 | semidirect |
| 224. #1533 | D53 | semidirect |
| 260. C53 | #10018 | semidirect |
| 306. #97 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285179 | 2 |
| #20284807 | 2 |
| #20280568 | 2 |
| #20273263 | 2 |
| #20273157 | 2 |
| #20272581 | 2 |
| C53×#1533 | 2 |
| #10018 | 53 |