Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
512 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 218 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. #20296032 | C2 | direct (N × H) |
| 4. C2×#16812766 | C2 | semidirect |
| 5. C2×C4⋊#11724786 | C2 | semidirect |
| 14. #16812766 | C22 | semidirect |
| 15. C4⋊#11724786 | C22 | semidirect |
| 78. C2×C109 | #424 | semidirect |
| 82. C109 | C2×#424 | semidirect |
| 160. C2 | #20296032 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182038 | 2 |
| C23×#11724786 | 2 |
| #20296032 | 2 |
| C2×#16812766 | 2 |
| C2×C4⋊#11724786 | 2 |
| C2×#16812655 | 2 |
| C2×#424 | 109 |