Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
432 conjugacy classes of subgroups; only the 204 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 204 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. Q8×#11724786 | C2 | semidirect |
| 2. #20296054 | C2 | semidirect |
| 3. #20296044 | C2 | semidirect |
| 4. D109⋊(C4⋊C8) | C2 | semidirect |
| 22. #13182030 | C8 | semidirect |
| 36. Q8×C109 | C2×C8 | semidirect |
| 43. D436 | C2×C8 | semidirect |
| 47. C4×D109 | C2×C8 | semidirect |
| 66. C109 | #2988 | semidirect |
| 102. Q8 | D109⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11724786 | 2 |
| #20296054 | 2 |
| #20296044 | 2 |
| D109⋊(C4⋊C8) | 2 |
| C4×#13182030 | 2 |
| #2988 | 109 |