Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#16812730 | C2 | semidirect |
| 3. C2×#16812626 | C2 | semidirect |
| 4. C2×#16812625 | C2 | semidirect |
| 5. #20294933 | C2 | semidirect |
| 6. #20294794 | C2 | semidirect |
| 7. C2×#137×C109 | C2 | semidirect |
| 45. #13182013 | D4 | semidirect |
| 64. C2×Q8×C109 | D4 | semidirect |
| 73. M16×C109 | D4 | semidirect |
| 145. C109 | #2007 | semidirect |
| 147. C2×#137 | D109 | semidirect |
| 191. C2×Q8 | C22⋊D109 | semidirect |
| 210. M16 | C22⋊D109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812730 | 2 |
| #20295604 | 2 |
| C2×#16812626 | 2 |
| C2×#16812625 | 2 |
| #20294933 | 2 |
| #20294794 | 2 |
| C2×#137×C109 | 2 |
| #2007 | 109 |