Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×#16812640 | C2 | semidirect |
| 2. C22×#13182004 | C2 | semidirect |
| 3. #20295262 | C2 | semidirect |
| 4. #20294851 | C2 | semidirect |
| 5. #20294827 | C2 | semidirect |
| 6. #20294826 | C2 | semidirect |
| 7. #466×C109 | C2 | semidirect |
| 28. #13182004 | D4 | semidirect |
| 63. C22×C109 | D16 | semidirect |
| 80. C109 | #2215 | semidirect |
| 84. #466 | D109 | semidirect |
| 146. C22 | #16812640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812640 | 2 |
| C22×#13182004 | 2 |
| #20295262 | 2 |
| #20294851 | 2 |
| #20294827 | 2 |
| #20294826 | 2 |
| #466×C109 | 2 |
| #2215 | 109 |