Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
912 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20285653 | C2 | semidirect |
| 3. #20275693 | C2 | semidirect |
| 4. #20273383 | C2 | semidirect |
| 5. #20273382 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 7. C53×#3208 | C2 | semidirect |
| 48. C4⋊#88322 | D4 | semidirect |
| 56. C4⋊Q8×C53 | D4 | semidirect |
| 57. C4⋊Q8×C53 | D4 | semidirect |
| 69. C4⋊C8×C53 | D4 | semidirect |
| 122. C4×Dic53 | SD16 | semidirect |
| 194. #3208 | D53 | semidirect |
| 227. C53 | #10290 | semidirect |
| 238. C4⋊Q8 | C22⋊D53 | semidirect |
| 239. C4⋊Q8 | C22⋊D53 | semidirect |
| 265. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285653 | 2 |
| #20283109 | 2 |
| #20275693 | 2 |
| #20273383 | 2 |
| #20273382 | 2 |
| #20272547 | 2 |
| C53×#3208 | 2 |
| #10290 | 53 |