Finite Group DatabasebetaFinite Group DatabasebetaOrder 13952.
500 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 229 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. C2×#16812706 | C2 | semidirect |
| 2. #20295104 | C2 | semidirect |
| 3. D4×#11724784 | C2 | semidirect |
| 4. #20295050 | C2 | semidirect |
| 5. #20294993 | C2 | semidirect |
| 6. C2×C4×#11724784 | C2 | semidirect |
| 29. C2×#11724784 | D4 | semidirect |
| 76. C4×C109 | #131 | semidirect |
| 84. C109 | #2931 | semidirect |
| 160. C4 | #16812706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812706 | 2 |
| #20295104 | 2 |
| D4×#11724784 | 2 |
| #20295050 | 2 |
| #20294993 | 2 |
| C2×C4×#11724784 | 2 |
| #532×C109 | 2 |
| #2931 | 109 |