Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
654 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 83 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. #20285714 | C2 | semidirect |
| 2. #20284810 | C2 | semidirect |
| 4. #20273312 | C2 | semidirect |
| 5. #20273159 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 7. C53×#1986 | C2 | semidirect |
| 60. C4⋊#88322 | D4 | semidirect |
| 68. #13133128 | D4 | semidirect |
| 70. C4⋊Q8×C53 | D4 | semidirect |
| 71. C4⋊Q8×C53 | D4 | semidirect |
| 224. #1986 | D53 | semidirect |
| 260. C53 | #10008 | semidirect |
| 270. C4⋊Q8 | D212 | semidirect |
| 271. C4⋊Q8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285714 | 2 |
| #20284810 | 2 |
| #20279649 | 2 |
| #20273312 | 2 |
| #20273159 | 2 |
| #20272571 | 2 |
| C53×#1986 | 2 |
| #10008 | 53 |