Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20285630 | C2 | semidirect |
| 2. #20279661 | C2 | semidirect |
| 3. #20273384 | C2 | semidirect |
| 4. #20273210 | C2 | semidirect |
| 5. #20273106 | C2 | semidirect |
| 6. #20272616 | C2 | semidirect |
| 7. C53×#3036 | C2 | semidirect |
| 47. C4⋊#88322 | D4 | semidirect |
| 62. C4⋊Q8×C53 | D4 | semidirect |
| 63. #127×C53 | D4 | semidirect |
| 77. C4⋊C8×C53 | D4 | semidirect |
| 96. C2×D4×C53 | D8 | semidirect |
| 234. #3036 | D53 | semidirect |
| 271. C53 | #10238 | semidirect |
| 285. C4⋊Q8 | C22⋊D53 | semidirect |
| 292. #127 | C22⋊D53 | semidirect |
| 312. C4⋊C8 | C22⋊D53 | semidirect |
| 352. C2×D4 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285630 | 2 |
| #20279661 | 2 |
| #20273384 | 2 |
| #20273210 | 2 |
| #20273106 | 2 |
| #20272616 | 2 |
| C53×#3036 | 2 |
| #10238 | 53 |