Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#13182019 | C2 | semidirect |
| 3. #20295405 | C2 | semidirect |
| 4. #20295265 | C2 | semidirect |
| 5. #20295236 | C2 | semidirect |
| 6. #20295233 | C2 | semidirect |
| 7. #20295182 | C2 | semidirect |
| 8. #20295181 | C2 | semidirect |
| 9. C4×#13182019 | C2 | semidirect |
| 52. #13182019 | D4 | direct (N × H) |
| 88. D4×C109 | Q16 | semidirect |
| 113. C22×C109 | C2×Q16 | semidirect |
| 120. C4×C109 | C2×Q16 | semidirect |
| 131. C109 | D4×Q16 | semidirect |
| 224. D4 | #13182019 | direct (N × H) |
| 244. C22 | C2×#13182019 | semidirect |
| 254. C4 | C2×#13182019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13182019 | 2 |
| D4×Dic218 | 2 |
| #20295405 | 2 |
| #20295265 | 2 |
| #20295236 | 2 |
| #20295233 | 2 |
| #20295182 | 2 |
| #20295181 | 2 |
| C4×#13182019 | 2 |
| D4×#11724784 | 2 |
| D4×Q8×C109 | 2 |
| D4×Q16 | 109 |