Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
324 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20296104 | C2 | semidirect |
| 2. #20296024 | C2 | semidirect |
| 3. #20296018 | C2 | semidirect |
| 4. D109⋊#100 | C2 | semidirect |
| 5. #20295908 | C2 | semidirect |
| 6. #20295895 | C2 | semidirect |
| 22. C2×#13182018 | C4 | semidirect |
| 23. C2×#13182017 | C4 | semidirect |
| 24. C2×#13182014 | C4 | semidirect |
| 26. C2×D8×C109 | C4 | semidirect |
| 126. C109 | #1903 | semidirect |
| 141. C2×D8 | #89137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296104 | 2 |
| #20296024 | 2 |
| #20296018 | 2 |
| D109⋊#100 | 2 |
| #20295908 | 2 |
| #20295895 | 2 |
| C2×#16812723 | 2 |
| #1903 | 109 |