Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
662 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 270 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. #20291094 | C2 | semidirect |
| 2. #20291072 | C2 | semidirect |
| 3. D53⋊(C22⋊C16) | C2 | semidirect |
| 5. C2×D53⋊C16 | C22 | semidirect |
| 6. C4⋊#11719910 | C22 | semidirect |
| 7. #16811518 | C22 | semidirect |
| 9. C4×#11719910 | C22 | semidirect |
| 41. C2×D212 | C16 | semidirect |
| 64. C22×D53 | C2×C16 | semidirect |
| 69. C2×C4×C53 | C2×C16 | semidirect |
| 76. D212 | C2×C16 | semidirect |
| 120. C53 | #33486 | semidirect |
| 179. C2×C4 | D53⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291094 | 2 |
| #20291072 | 2 |
| D53⋊(C22⋊C16) | 2 |
| C2×#16810688 | 2 |
| #33486 | 53 |