Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 5. #16811501 | C4 | semidirect |
| 8. C2×#13133128 | C4 | semidirect |
| 9. C2×C4⋊C8×C53 | C4 | semidirect |
| 101. C2×C4⋊C8 | #6157 | semidirect |
| 107. C53 | #7283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133276 | 2 |
| #20275512 | 2 |
| #7283 | 53 |