Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
224 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 3. #20295867 | C2 | semidirect |
| 4. C8×#11724786 | C2 | semidirect |
| 24. #13182013 | C8 | semidirect |
| 31. M16×C109 | C8 | semidirect |
| 46. #11724786 | M16 | direct (N × H) |
| 47. C8×C109 | C2×C8 | semidirect |
| 48. #11724784 | C2×C8 | semidirect |
| 65. C109 | C8×M16 | semidirect |
| 87. M16 | #11724786 | direct (N × H) |
| 113. C8 | C2×#11724786 | semidirect |
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 |
| #20295867 | 2 |
| C8×#11724786 | 2 |
| M16×Dic109 | 2 |
| C8×M16 | 109 |