Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
254 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #20272781 | C2 | semidirect |
| 4. #20272780 | C2 | semidirect |
| 5. C53×#1368 | C2 | semidirect |
| 24. C16×D53 | C8 | semidirect |
| 50. C16×C53 | C2×C8 | semidirect |
| 52. #11719908 | C2×C8 | semidirect |
| 81. #1368 | D53 | direct (N × H) |
| 84. D53 | #1368 | direct (N × H) |
| 96. C53 | C2×#1368 | semidirect |
| 132. C16 | C8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #346×D53 | 2 |
| #334×D53 | 2 |
| #20272781 | 2 |
| #20272780 | 2 |
| C53×#1368 | 2 |
| C2×#1368 | 53 |