Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
230 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #20273534 | C2 | semidirect |
| 3. #20272781 | C2 | semidirect |
| 4. #20272685 | C2 | semidirect |
| 6. #20272635 | C2 | semidirect |
| 36. SD32×C53 | C8 | semidirect |
| 48. Q16×C53 | C2×C8 | semidirect |
| 65. C16×C53 | C2×C8 | semidirect |
| 125. C53 | #12065 | semidirect |
| 131. SD32 | #88322 | semidirect |
| 151. Q16 | C2×#88322 | semidirect |
| 169. C16 | C2×#88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20273539 | 2 |
| #20273534 | 2 |
| #20272781 | 2 |
| #20272685 | 2 |
| #20272682 | 2 |
| #20272635 | 2 |
| C53×#2175 | 2 |
| #12065 | 53 |