Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 106 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. #20291074 | C2 | semidirect |
| 2. D53⋊(C4⋊C16) | C2 | semidirect |
| 3. Q8⋊#11719910 | C2 | semidirect |
| 4. #20289666 | C2 | semidirect |
| 57. #11719949 | C16 | semidirect |
| 97. Q8×C53 | C2×C16 | semidirect |
| 109. D212 | C2×C16 | semidirect |
| 172. C53 | #11621 | semidirect |
| 247. Q8 | D53⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291074 | 2 |
| D53⋊(C4⋊C16) | 2 |
| Q8⋊#11719910 | 2 |
| #20289666 | 2 |
| C8×#11719949 | 2 |
| #11621 | 53 |