Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
432 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 432 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×C22⋊#11715895 | C2 | semidirect |
| 3. C2×#15690722 | C2 | semidirect |
| 4. #20260489 | C2 | semidirect |
| 5. C23×C8×C97 | C2 | semidirect |
| 24. C2×C22⋊D97 | C8 | semidirect |
| 50. C2×C8×C97 | D4 | semidirect |
| 61. C22×D97 | C2×C8 | semidirect |
| 78. C2×Dic97 | C2×C8 | semidirect |
| 88. C22×C97 | C22⋊C8 | semidirect |
| 114. C97 | #1869 | semidirect |
| 115. C23×C8 | D97 | semidirect |
| 159. C2×C8 | C22⋊D97 | semidirect |
| 207. C22 | #15690722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D97 | 2 |
| C2×C22⋊#11715895 | 2 |
| C2×#15690722 | 2 |
| #20260489 | 2 |
| C23×C8×C97 | 2 |
| #1869 | 97 |