Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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×#16812624 | C2 | semidirect |
| 3. C2×#16812622 | C2 | semidirect |
| 4. C2×#16812620 | C2 | semidirect |
| 5. C2×#16812611 | C2 | semidirect |
| 6. #20294883 | C2 | semidirect |
| 7. C2×#102×C109 | C2 | semidirect |
| 13. C2×#13182028 | C4 | semidirect |
| 94. D4×C109 | C22⋊C4 | semidirect |
| 122. Dic218 | C22⋊C4 | semidirect |
| 164. C109 | #1788 | semidirect |
| 169. C2×#102 | D109 | semidirect |
| 263. D4 | #13182006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182028 | 2 |
| C2×#16812624 | 2 |
| C2×#16812622 | 2 |
| C2×#16812620 | 2 |
| C2×#16812611 | 2 |
| #20294883 | 2 |
| C2×#102×C109 | 2 |
| #1788 | 109 |