Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
802 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20277545 | C2 | semidirect |
| 2. #20275552 | C2 | semidirect |
| 3. #20274659 | C2 | semidirect |
| 4. #20273231 | C2 | semidirect |
| 5. #20272620 | C2 | semidirect |
| 6. #20272600 | C2 | semidirect |
| 22. C2×AGL(1,ℤ/8)×C53 | C4 | semidirect |
| 27. C53×#417 | C4 | semidirect |
| 57. C22×D4×C53 | C2×C4 | semidirect |
| 64. C2×M16×C53 | C2×C4 | semidirect |
| 69. C2×C4⋊C4×C53 | C2×C4 | semidirect |
| 165. D4×C53 | #99 | semidirect |
| 247. C2×AGL(1,ℤ/8) | Dic53 | semidirect |
| 254. #417 | Dic53 | semidirect |
| 267. C53 | #9365 | semidirect |
| 276. C22×D4 | C2×Dic53 | semidirect |
| 285. C2×M16 | C2×Dic53 | semidirect |
| 292. C2×C4⋊C4 | C2×Dic53 | semidirect |
| 404. D4 | #13133132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277545 | 2 |
| #20275552 | 2 |
| #20274659 | 2 |
| #20273231 | 2 |
| #20272620 | 2 |
| #20272600 | 2 |
| C53×#3006 | 2 |
| #9365 | 53 |