Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
254 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 2. #20289741 | C2 | semidirect |
| 3. #20289740 | C2 | semidirect |
| 4. #20289739 | C2 | semidirect |
| 27. C16×D53 | C8 | semidirect |
| 50. C16×C53 | C2×C8 | semidirect |
| 52. #11719908 | C2×C8 | semidirect |
| 84. D53 | #1368 | semidirect |
| 96. C53 | C2×#1368 | semidirect |
| 132. C16 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#334 | 2 |
| #20289741 | 2 |
| #20289740 | 2 |
| #20289739 | 2 |
| #346×D53 | 2 |
| C2×#1368 | 53 |