Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
686 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 686 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. #20284715 | C2 | semidirect |
| 2. #20284181 | C2 | semidirect |
| 3. #20279616 | C2 | semidirect |
| 4. #20273276 | C2 | semidirect |
| 5. #20273105 | C2 | semidirect |
| 6. #20272575 | C2 | semidirect |
| 7. C53×#1486 | C2 | semidirect |
| 42. #13133217 | D4 | semidirect |
| 43. #13133214 | D4 | semidirect |
| 67. C4×#88322 | D4 | semidirect |
| 83. C4⋊C8×C53 | D4 | semidirect |
| 119. C2×D212 | D8 | semidirect |
| 253. #1486 | D53 | semidirect |
| 289. C53 | #9996 | semidirect |
| 331. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284715 | 2 |
| #20284181 | 2 |
| #20279616 | 2 |
| #20273276 | 2 |
| #20273105 | 2 |
| #20272575 | 2 |
| C53×#1486 | 2 |
| #9996 | 53 |