Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
248 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 1. #20289539 | C2 | semidirect |
| 18. C4⋊Q8×C53 | C8 | semidirect |
| 19. #127×C53 | C8 | semidirect |
| 91. C53 | #7115 | semidirect |
| 94. C4⋊Q8 | #88324 | semidirect |
| 95. #127 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289539 | 2 |
| #20275548 | 2 |
| #7115 | 53 |