Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
300 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 21. C4×Dic97 | C8 | semidirect |
| 55. C4×C97 | C4⋊C8 | semidirect |
| 60. Dic97 | C4⋊C8 | semidirect |
| 67. C97 | #1842 | semidirect |
| 124. C4 | #15690739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11715895 | 2 |
| C2×#15690739 | 2 |
| C42×Dic97 | 2 |
| C2×C4⋊C8×C97 | 2 |
| #1842 | 97 |