Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
848 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 133 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×#15690730 | C2 | semidirect |
| 3. C2×C22⋊#11715895 | C2 | semidirect |
| 4. #380×C97 | C2 | semidirect |
| 9. C22×D388 | C4 | semidirect |
| 11. C22×#11715895 | C22 | semidirect |
| 15. C2×C4⋊C4×C97 | C22 | semidirect |
| 72. D388 | C22⋊C4 | semidirect |
| 78. C22×C97 | #102 | semidirect |
| 102. C97 | #1786 | semidirect |
| 106. #380 | D97 | semidirect |
| 115. C2×C4⋊C4 | C2×D97 | semidirect |
| 186. C22 | #15690730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D388 | 2 |
| C2×#15690730 | 2 |
| C2×C22⋊#11715895 | 2 |
| #380×C97 | 2 |
| #1786 | 97 |