Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16812722 | C2 | semidirect |
| 2. C2×Q16×D109 | C2 | semidirect |
| 3. #20295688 | C2 | semidirect |
| 4. #20295410 | C2 | semidirect |
| 5. #20295268 | C2 | semidirect |
| 6. #20295263 | C2 | semidirect |
| 7. #20295248 | C2 | semidirect |
| 8. #20295191 | C2 | semidirect |
| 9. #20295166 | C2 | semidirect |
| 10. C8×D436 | C2 | semidirect |
| 11. C4×Q16×C109 | C2 | semidirect |
| 73. Q16×C109 | D4 | semidirect |
| 120. C2×D109 | #135 | semidirect |
| 137. C109 | #3285 | semidirect |
| 147. C4×Q16 | D109 | semidirect |
| 195. Q16 | D436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812722 | 2 |
| C2×Q16×D109 | 2 |
| #20295688 | 2 |
| #20295410 | 2 |
| #20295268 | 2 |
| #20295263 | 2 |
| #20295248 | 2 |
| #20295191 | 2 |
| #20295166 | 2 |
| C8×D436 | 2 |
| C4×Q16×C109 | 2 |
| #3285 | 109 |