Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
680 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 338 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 |
|---|---|---|
| 2. #20295985 | C2 | direct (N × H) |
| 3. C2×#16812754 | C2 | semidirect |
| 5. C2×D109⋊C8 | C4 | semidirect |
| 8. #16812754 | C22 | semidirect |
| 16. D109⋊C8 | C2×C4 | semidirect |
| 17. C2×#11724786 | C2×C4 | semidirect |
| 49. #11724786 | C22×C4 | semidirect |
| 53. C2×D109 | #97 | semidirect |
| 61. C2×C109 | C2×#97 | semidirect |
| 64. D109 | C2×#97 | semidirect |
| 66. C109 | C22×#97 | semidirect |
| 128. C2 | #20295985 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D109⋊C8 | 2 |
| #20295985 | 2 |
| C2×#16812754 | 2 |
| C2×C42×D109 | 2 |
| C22×#97 | 109 |