Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
752 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 254 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 |
|---|---|---|
| 7. C2×C4×#89137 | C4 | semidirect |
| 8. (C2×#89137)⋊C4 | C4 | direct (N × H) |
| 11. C2×C4×Dic109 | C4 | semidirect |
| 12. C2×C4×Dic109 | C4 | semidirect |
| 14. C2×C42×C109 | C4 | semidirect |
| 47. C2×#89137 | C42 | semidirect |
| 51. C2×C4×C109 | C42 | semidirect |
| 57. C2×Dic109 | C42 | semidirect |
| 77. C4×C109 | #95 | semidirect |
| 79. Dic109 | #95 | semidirect |
| 88. C109 | C4×#95 | semidirect |
| 101. C2×C42 | #89137 | semidirect |
| 148. C2×C4 | C4×#89137 | semidirect |
| 167. C4 | (C2×#89137)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#89137 | 2 |
| C2×(C2×#89137)⋊C4 | 2 |
| C2×C42×D109 | 2 |
| C4×#95 | 109 |