Finite Group DatabasebetaFinite Group DatabasebetaOrder 12736.
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×#15691869 | C2 | semidirect |
| 3. C2×C8×D199 | C2 | semidirect |
| 4. C22⋊(C199⋊C8) | C2 | semidirect |
| 5. (C2×D199)⋊C8 | C2 | semidirect |
| 6. (C2×D199)⋊C8 | C2 | semidirect |
| 7. C22⋊C8×C199 | C2 | semidirect |
| 65. C199 | #408 | semidirect |
| 73. C22⋊C8 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691886 | 2 |
| C2×#15691869 | 2 |
| C2×C8×D199 | 2 |
| C22⋊(C199⋊C8) | 2 |
| (C2×D199)⋊C8 | 2 |
| C22⋊C8×C199 | 2 |
| #408 | 199 |