Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 1. C22×C4⋊Dic97 | C2 | semidirect |
| 2. C2×#15690731 | C2 | semidirect |
| 3. C2×C22⋊#11715895 | C2 | semidirect |
| 4. #20260497 | C2 | semidirect |
| 17. #121×C97 | C4 | semidirect |
| 29. C4⋊Dic97 | D4 | semidirect |
| 38. C2×D4×C97 | C2×C4 | semidirect |
| 47. C4⋊C4×C97 | C2×C4 | semidirect |
| 97. C22×C97 | #102 | semidirect |
| 120. C97 | #1874 | semidirect |
| 132. #121 | Dic97 | semidirect |
| 148. C2×D4 | C2×Dic97 | semidirect |
| 167. C4⋊C4 | C2×Dic97 | semidirect |
| 217. C22 | #15690731 | 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×#15690731 | 2 |
| C2×C22⋊#11715895 | 2 |
| #20260497 | 2 |
| C2×#121×C97 | 2 |
| #1874 | 97 |