Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
878 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 283 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. #20274331 | C2 | direct (N × H) |
| 62. C2×#88322 | Q16 | semidirect |
| 81. #88322 | C2×Q16 | semidirect |
| 97. C2×C53 | #1713 | semidirect |
| 114. C53 | C2×#1713 | semidirect |
| 186. C2 | #20274331 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811026 | 2 |
| C2×#16811003 | 2 |
| #20274331 | 2 |
| C2×C8×#88322 | 2 |
| C2×C53×#494 | 2 |
| C2×#1713 | 53 |