Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
348 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×C4⋊#11724784 | C2 | semidirect |
| 4. #20294781 | C2 | semidirect |
| 36. C22⋊C4×C109 | C8 | semidirect |
| 55. C2×C4×C109 | C2×C8 | semidirect |
| 67. C22×C109 | C4⋊C8 | semidirect |
| 86. C109 | #1850 | semidirect |
| 122. C22⋊C4 | #11724784 | semidirect |
| 141. C2×C4 | C2×#11724784 | semidirect |
| 153. C22 | C4⋊#11724784 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11724784 | 2 |
| C2×C4⋊#11724784 | 2 |
| C2×C22⋊#11724784 | 2 |
| #20294781 | 2 |
| C4×C22⋊C4×C109 | 2 |
| #1850 | 109 |