Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
230 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20272780 | C2 | semidirect |
| 4. #20272685 | C2 | semidirect |
| 6. #20272636 | C2 | semidirect |
| 7. C53×#1579 | C2 | semidirect |
| 26. #13133160 | C8 | semidirect |
| 48. Q16×C53 | C2×C8 | semidirect |
| 66. #11719908 | C2×C8 | semidirect |
| 101. #1579 | D53 | semidirect |
| 125. C53 | #12065 | semidirect |
| 151. Q16 | C8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276577 | 2 |
| #20273540 | 2 |
| #20272780 | 2 |
| #20272685 | 2 |
| #20272681 | 2 |
| #20272636 | 2 |
| C53×#1579 | 2 |
| #12065 | 53 |