Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
182 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 2. #20295105 | C2 | semidirect |
| 3. #20294778 | C2 | semidirect |
| 4. D4⋊#11724784 | C2 | semidirect |
| 5. #20294753 | C2 | semidirect |
| 6. #20294747 | C2 | semidirect |
| 7. C8×D4×C109 | C2 | semidirect |
| 45. D4×C109 | M16 | semidirect |
| 59. C8×C109 | D8 | semidirect |
| 84. C109 | #1581 | semidirect |
| 87. C8×D4 | D109 | semidirect |
| 131. D4 | #13182012 | semidirect |
| 147. C8 | #13182014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13182014 | 2 |
| #20295105 | 2 |
| #20294778 | 2 |
| D4⋊#11724784 | 2 |
| #20294753 | 2 |
| #20294747 | 2 |
| C8×D4×C109 | 2 |
| #1581 | 109 |