Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20287851 | C2 | semidirect |
| 2. #20285161 | C2 | semidirect |
| 3. #20276444 | C2 | semidirect |
| 4. #20275608 | C2 | semidirect |
| 5. C53×#1375 | C2 | semidirect |
| 35. C2×Dic212 | D4 | semidirect |
| 41. C2×D424 | D4 | semidirect |
| 60. C2×C16×C53 | D4 | semidirect |
| 162. #1375 | D53 | semidirect |
| 186. C53 | #13340 | semidirect |
| 221. C2×C16 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287851 | 2 |
| #20285161 | 2 |
| #20276444 | 2 |
| #20275608 | 2 |
| C53×#1375 | 2 |
| #13340 | 53 |