Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 112 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. C2×#16811545 | C2 | semidirect |
| 2. C2×C8×#88324 | C2 | semidirect |
| 3. #20289678 | C2 | direct (N × H) |
| 8. #16811545 | C22 | semidirect |
| 10. C8×#88324 | C22 | semidirect |
| 29. #13133239 | C8 | semidirect |
| 31. C2×Dic212 | C8 | semidirect |
| 33. C2×D424 | C8 | semidirect |
| 83. Dic212 | C2×C8 | semidirect |
| 85. D424 | C2×C8 | semidirect |
| 143. C2×C53 | #1335 | semidirect |
| 161. C53 | C2×#1335 | semidirect |
| 281. C2 | #20289678 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811545 | 2 |
| C2×C8×#88324 | 2 |
| #20289678 | 2 |
| C2×#16810739 | 2 |
| C2×#1335 | 53 |