Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
840 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 205 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×#16812675 | C2 | semidirect |
| 3. #20294945 | C2 | semidirect |
| 4. #20294937 | C2 | semidirect |
| 5. #20294933 | C2 | semidirect |
| 7. #20294899 | C2 | semidirect |
| 8. #20294886 | C2 | semidirect |
| 9. C23×Q8×C109 | C2 | semidirect |
| 34. C2×C22⋊D109 | Q8 | semidirect |
| 55. C2×Q8×C109 | D4 | semidirect |
| 73. C22×D109 | C2×Q8 | semidirect |
| 95. C2×Dic109 | C2×Q8 | semidirect |
| 101. C22×C109 | C22⋊Q8 | semidirect |
| 127. C109 | #2409 | semidirect |
| 128. C23×Q8 | D109 | semidirect |
| 165. C2×Q8 | C22⋊D109 | semidirect |
| 233. C22 | #16812675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812675 | 2 |
| C2×C4×C22⋊D109 | 2 |
| #20294945 | 2 |
| #20294937 | 2 |
| #20294933 | 2 |
| #20294905 | 2 |
| #20294899 | 2 |
| #20294886 | 2 |
| C23×Q8×C109 | 2 |
| #2409 | 109 |