Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20285633 | C2 | semidirect |
| 2. #20284181 | C2 | semidirect |
| 3. #20279662 | C2 | semidirect |
| 4. #20273211 | C2 | semidirect |
| 5. #20273107 | C2 | semidirect |
| 6. #20272616 | C2 | semidirect |
| 7. C53×#1545 | C2 | semidirect |
| 40. #13133217 | D4 | semidirect |
| 41. #13133214 | D4 | semidirect |
| 59. C4⋊#88322 | D4 | semidirect |
| 77. C4⋊C8×C53 | D4 | semidirect |
| 115. C2×D212 | D8 | semidirect |
| 236. #1545 | D53 | semidirect |
| 271. C53 | #10238 | semidirect |
| 312. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285633 | 2 |
| #20284181 | 2 |
| #20279662 | 2 |
| #20273211 | 2 |
| #20273107 | 2 |
| #20272616 | 2 |
| C53×#1545 | 2 |
| #10238 | 53 |