Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
360 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
| 3. C2×#16812620 | C2 | semidirect |
| 4. C2×#16812619 | C2 | semidirect |
| 5. #20294928 | C2 | semidirect |
| 6. #20294788 | C2 | semidirect |
| 7. #390×C109 | C2 | semidirect |
| 88. C2×C4×C109 | D8 | semidirect |
| 143. C109 | #2054 | semidirect |
| 149. #390 | D109 | semidirect |
| 238. C2×C4 | #13182014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182014 | 2 |
| C2×C4⋊#11724784 | 2 |
| C2×#16812620 | 2 |
| C2×#16812619 | 2 |
| #20294928 | 2 |
| #20294788 | 2 |
| #390×C109 | 2 |
| #2054 | 109 |