Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15690739 | C2 | semidirect |
| 4. #20260489 | C2 | semidirect |
| 24. C22×Dic97 | C8 | semidirect |
| 85. C22×C97 | C4⋊C8 | semidirect |
| 99. Dic97 | C22⋊C8 | semidirect |
| 109. C97 | #1797 | semidirect |
| 194. C22 | #15690739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic97 | 2 |
| C2×#15690739 | 2 |
| C2×C22⋊#11715895 | 2 |
| #20260489 | 2 |
| C2×C22⋊C8×C97 | 2 |
| #1797 | 97 |