Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
346 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 1. #20295998 | C2 | semidirect |
| 2. C4×C22⋊#89137 | C2 | semidirect |
| 3. #20295878 | C2 | semidirect |
| 4. #20295877 | C2 | semidirect |
| 10. #16812756 | C22 | semidirect |
| 11. (C2×#89137)⋊C4 | C22 | semidirect |
| 13. C2×D4×D109 | C4 | semidirect |
| 16. #16812673 | C4 | semidirect |
| 20. C4⋊C4×D109 | C4 | semidirect |
| 22. #121×C109 | C4 | semidirect |
| 123. C109 | #1507 | semidirect |
| 138. #121 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295998 | 2 |
| C4×C22⋊#89137 | 2 |
| #20295878 | 2 |
| #20295877 | 2 |
| #121×D109 | 2 |
| #1507 | 109 |