Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
794 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20284175 | C2 | semidirect |
| 2. #20279662 | C2 | semidirect |
| 3. #20273383 | C2 | semidirect |
| 4. #20273210 | C2 | semidirect |
| 5. #20273105 | C2 | semidirect |
| 6. #20272617 | C2 | semidirect |
| 7. C53×#3205 | C2 | semidirect |
| 53. C4⋊#88322 | D4 | semidirect |
| 64. C4⋊Q8×C53 | D4 | semidirect |
| 69. #127×C53 | D4 | semidirect |
| 76. C4⋊C8×C53 | D4 | semidirect |
| 117. C2×D212 | D8 | semidirect |
| 233. #3205 | D53 | semidirect |
| 271. C53 | #10238 | semidirect |
| 285. C4⋊Q8 | C22⋊D53 | semidirect |
| 292. #127 | C22⋊D53 | semidirect |
| 312. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284175 | 2 |
| #20279662 | 2 |
| #20273383 | 2 |
| #20273210 | 2 |
| #20273105 | 2 |
| #20272617 | 2 |
| C53×#3205 | 2 |
| #10238 | 53 |