Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20295698 | C2 | semidirect |
| 3. #20295403 | C2 | semidirect |
| 4. #20295263 | C2 | semidirect |
| 5. #20295226 | C2 | semidirect |
| 6. #20295174 | C2 | semidirect |
| 7. C8×D436 | C2 | semidirect |
| 8. C4×Q16×C109 | C2 | semidirect |
| 48. Q16×C109 | D4 | semidirect |
| 88. C4×C109 | #135 | semidirect |
| 98. C109 | #3287 | semidirect |
| 105. C4×Q16 | D109 | semidirect |
| 138. Q16 | D436 | semidirect |
| 187. C4 | #16812722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812722 | 2 |
| #20295698 | 2 |
| #20295403 | 2 |
| #20295263 | 2 |
| #20295226 | 2 |
| #20295174 | 2 |
| C8×D436 | 2 |
| C4×Q16×C109 | 2 |
| #3287 | 109 |