Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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. #20295376 | C2 | semidirect |
| 3. #20295354 | C2 | semidirect |
| 4. #20295311 | C2 | semidirect |
| 5. #20295257 | C2 | semidirect |
| 6. #20295228 | C2 | semidirect |
| 7. #20295165 | C2 | semidirect |
| 8. C4×#13182016 | C2 | semidirect |
| 9. D4×#11724784 | C2 | semidirect |
| 10. C2×#16812623 | C2 | semidirect |
| 11. D4×Q8×C109 | C2 | semidirect |
| 83. Q8×C109 | #41 | semidirect |
| 84. D4×C109 | SD16 | semidirect |
| 129. C109 | #3298 | semidirect |
| 130. D4×Q8 | D109 | semidirect |
| 213. Q8 | #13182028 | semidirect |
| 217. D4 | #13182016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20295680 | 2 |
| #20295376 | 2 |
| #20295354 | 2 |
| #20295311 | 2 |
| #20295257 | 2 |
| #20295228 | 2 |
| #20295165 | 2 |
| C4×#13182016 | 2 |
| D4×#11724784 | 2 |
| C2×#16812623 | 2 |
| D4×Q8×C109 | 2 |
| #3298 | 109 |