Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
196 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20296054 | C2 | semidirect |
| 2. D4×#11724786 | C2 | semidirect |
| 3. #20295890 | C2 | semidirect |
| 4. #20295874 | C2 | semidirect |
| 5. D4⋊#11724786 | C2 | semidirect |
| 6. C8×#11724786 | C2 | semidirect |
| 33. #13182014 | C8 | semidirect |
| 45. D4×C109 | C2×C8 | semidirect |
| 54. D436 | C2×C8 | semidirect |
| 61. #11724786 | D8 | semidirect |
| 63. #11724784 | C2×C8 | semidirect |
| 84. C109 | C8×D8 | semidirect |
| 131. D4 | D109⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20296054 | 2 |
| D4×#11724786 | 2 |
| #20295890 | 2 |
| #20295874 | 2 |
| D4⋊#11724786 | 2 |
| C8×#11724786 | 2 |
| #20295106 | 2 |
| C8×D8 | 109 |