Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
180 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
| 3. #20295887 | C2 | semidirect |
| 4. Q8⋊#11724786 | C2 | semidirect |
| 6. C8×#11724786 | C2 | semidirect |
| 39. SD16×C109 | C8 | semidirect |
| 43. Q8×C109 | C2×C8 | semidirect |
| 58. #11724786 | SD16 | direct (N × H) |
| 59. C8×C109 | C2×C8 | semidirect |
| 78. C109 | C8×SD16 | semidirect |
| 104. SD16 | #11724786 | direct (N × H) |
| 121. Q8 | C2×#11724786 | semidirect |
| 138. C8 | C2×#11724786 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11724786 | 2 |
| D4×#11724786 | 2 |
| #20295887 | 2 |
| Q8⋊#11724786 | 2 |
| D4⋊#11724786 | 2 |
| C8×#11724786 | 2 |
| SD16×Dic109 | 2 |
| C8×SD16 | 109 |