Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
254 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 99 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. D8×#88322 | C2 | semidirect |
| 2. #20272789 | C2 | semidirect |
| 3. #20272676 | C2 | semidirect |
| 4. #20272631 | C2 | semidirect |
| 24. D16×C53 | C8 | semidirect |
| 33. D8×C53 | C2×C8 | semidirect |
| 44. C16×C53 | C2×C8 | semidirect |
| 90. C53 | #12045 | semidirect |
| 94. D16 | #88322 | semidirect |
| 108. D8 | C2×#88322 | semidirect |
| 120. C16 | C2×#88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#88322 | 2 |
| #20272789 | 2 |
| #20272676 | 2 |
| #20272631 | 2 |
| C4×D16×C53 | 2 |
| #12045 | 53 |