Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
528 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 274 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. #20296042 | C2 | direct (N × H) |
| 2. C2×C4⋊#11724786 | C2 | semidirect |
| 4. C2×C4×#11724786 | C2 | semidirect |
| 7. C4⋊#11724786 | C22 | semidirect |
| 9. C4×#11724786 | C22 | semidirect |
| 37. C22×C4×C109 | C8 | semidirect |
| 48. C2×C4×C109 | C2×C8 | semidirect |
| 80. C2×C109 | #431 | semidirect |
| 85. C109 | C2×#431 | semidirect |
| 114. C22×C4 | #11724786 | semidirect |
| 145. C2×C4 | C2×#11724786 | semidirect |
| 165. C2 | #20296042 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296042 | 2 |
| C2×C4⋊#11724786 | 2 |
| C2×C22⋊#11724786 | 2 |
| C2×C4×#11724786 | 2 |
| C22×C4×Dic109 | 2 |
| C2×#431 | 109 |