Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
576 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20284810 | C2 | semidirect |
| 3. #20273339 | C2 | semidirect |
| 4. #20273266 | C2 | semidirect |
| 5. #20273159 | C2 | semidirect |
| 6. #20272580 | C2 | semidirect |
| 7. C53×#3140 | C2 | semidirect |
| 53. #13133128 | D4 | semidirect |
| 61. C4⋊Q8×C53 | D4 | semidirect |
| 62. C4⋊Q8×C53 | D4 | semidirect |
| 81. C4×C8×C53 | D4 | semidirect |
| 205. #3140 | D53 | semidirect |
| 243. C53 | #10022 | semidirect |
| 251. C4⋊Q8 | C22⋊D53 | semidirect |
| 252. C4⋊Q8 | C22⋊D53 | semidirect |
| 288. C4×C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284810 | 2 |
| #20280568 | 2 |
| #20273339 | 2 |
| #20273266 | 2 |
| #20273159 | 2 |
| #20272580 | 2 |
| C53×#3140 | 2 |
| #10022 | 53 |