Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
692 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 85 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. #20284802 | C2 | semidirect |
| 2. #20279655 | C2 | semidirect |
| 3. #20275635 | C2 | semidirect |
| 4. #20273313 | C2 | semidirect |
| 5. #20273157 | C2 | semidirect |
| 6. #20272572 | C2 | semidirect |
| 7. C53×#3213 | C2 | semidirect |
| 58. #13133128 | D4 | semidirect |
| 66. C4⋊Q8×C53 | D4 | semidirect |
| 67. #127×C53 | D4 | semidirect |
| 80. C4⋊C8×C53 | D4 | semidirect |
| 231. #3213 | D53 | semidirect |
| 271. C53 | #10004 | semidirect |
| 282. C4⋊Q8 | C22⋊D53 | semidirect |
| 283. #127 | C22⋊D53 | semidirect |
| 311. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284802 | 2 |
| #20279655 | 2 |
| #20275635 | 2 |
| #20273313 | 2 |
| #20273157 | 2 |
| #20272572 | 2 |
| C53×#3213 | 2 |
| #10004 | 53 |