Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
440 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 234 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. #20296075 | C2 | direct (N × H) |
| 23. C2×#11724786 | Q8 | semidirect |
| 27. C2×Dic218 | C8 | semidirect |
| 53. Dic218 | C2×C8 | semidirect |
| 56. #11724786 | C2×Q8 | semidirect |
| 68. C2×C109 | C8×Q8 | semidirect |
| 73. C109 | C2×C8×Q8 | semidirect |
| 141. C2 | #20296075 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296075 | 2 |
| C2×#16812766 | 2 |
| C2×C4⋊#11724786 | 2 |
| C2×C4×#11724786 | 2 |
| C2×#16812664 | 2 |
| C2×C8×Q8 | 109 |