Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
632 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20284508 | C2 | semidirect |
| 3. #20273279 | C2 | semidirect |
| 4. #20273140 | C2 | semidirect |
| 5. #20273107 | C2 | semidirect |
| 6. #20272574 | C2 | semidirect |
| 7. C53×#3101 | C2 | semidirect |
| 52. C4⋊#88322 | D4 | semidirect |
| 63. C4⋊Q8×C53 | D4 | semidirect |
| 64. C4⋊Q8×C53 | D4 | semidirect |
| 83. C4×C8×C53 | D4 | semidirect |
| 111. C2×D212 | SD16 | semidirect |
| 231. #3101 | D53 | semidirect |
| 270. C53 | #10000 | semidirect |
| 278. C4⋊Q8 | C22⋊D53 | semidirect |
| 279. C4⋊Q8 | C22⋊D53 | semidirect |
| 318. C4×C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284508 | 2 |
| #20279616 | 2 |
| #20273279 | 2 |
| #20273140 | 2 |
| #20273107 | 2 |
| #20272574 | 2 |
| C53×#3101 | 2 |
| #10000 | 53 |