Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
630 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 124 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. #20291562 | C2 | semidirect |
| 2. #20290014 | C2 | semidirect |
| 3. #20289955 | C2 | semidirect |
| 4. #20289539 | C2 | semidirect |
| 28. C4×#88324 | D4 | semidirect |
| 50. #127×C53 | C8 | semidirect |
| 63. C2×D4×C53 | C2×C8 | semidirect |
| 81. C42×C53 | C2×C8 | semidirect |
| 184. C53 | #9101 | semidirect |
| 192. #127 | #88324 | semidirect |
| 227. C2×D4 | C2×#88324 | semidirect |
| 255. C42 | C2×#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291562 | 2 |
| #20290014 | 2 |
| #20289955 | 2 |
| #20289539 | 2 |
| #20277441 | 2 |
| #9101 | 53 |