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×#16812623 | C2 | semidirect |
| 3. C2×#16812621 | C2 | semidirect |
| 4. C2×#16812619 | C2 | semidirect |
| 5. C2×#16812611 | C2 | semidirect |
| 6. #20294883 | C2 | semidirect |
| 7. C2×#103×C109 | C2 | semidirect |
| 13. C2×#13182030 | C4 | semidirect |
| 94. Q8×C109 | C22⋊C4 | semidirect |
| 117. D436 | C22⋊C4 | semidirect |
| 164. C109 | #1788 | semidirect |
| 167. C2×#103 | D109 | semidirect |
| 258. Q8 | #13182006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182030 | 2 |
| C2×#16812623 | 2 |
| C2×#16812621 | 2 |
| C2×#16812619 | 2 |
| C2×#16812611 | 2 |
| #20294883 | 2 |
| C2×#103×C109 | 2 |
| #1788 | 109 |