Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
442 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×C4×#89137 | C2 | semidirect |
| 2. C2×#16812764 | C2 | semidirect |
| 3. #20295997 | C2 | semidirect |
| 4. #20295896 | C2 | semidirect |
| 17. #16812675 | C4 | semidirect |
| 18. #16812674 | C4 | semidirect |
| 19. #16812673 | C4 | semidirect |
| 24. C22⋊Q8×C109 | C4 | semidirect |
| 34. C4×#89137 | D4 | semidirect |
| 40. C2×D436 | C2×C4 | semidirect |
| 50. C4⋊Dic109 | C2×C4 | semidirect |
| 57. C2×Q8×C109 | C2×C4 | semidirect |
| 60. C4⋊C4×C109 | C2×C4 | semidirect |
| 99. C22×C109 | #104 | semidirect |
| 110. C2×D109 | #104 | semidirect |
| 130. C109 | #1896 | semidirect |
| 142. C22⋊Q8 | #89137 | semidirect |
| 158. C2×Q8 | C2×#89137 | semidirect |
| 182. C4⋊C4 | C2×#89137 | semidirect |
| 241. C22 | #16812764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#89137 | 2 |
| C2×#16812764 | 2 |
| #20295997 | 2 |
| #20295896 | 2 |
| #20295539 | 2 |
| #1896 | 109 |