Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
1088 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 206 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×(C2×#87604)⋊C4 | C2 | semidirect |
| 7. C2×C22⋊#87604 | C4 | semidirect |
| 10. C23×Dic97 | C4 | semidirect |
| 13. C22×C4×D97 | C4 | semidirect |
| 15. C23×C4×C97 | C4 | semidirect |
| 20. C22×#87604 | C2×C4 | semidirect |
| 76. C2×C4×C97 | C22⋊C4 | semidirect |
| 80. C2×Dic97 | C22⋊C4 | semidirect |
| 87. C22×C97 | #95 | semidirect |
| 99. C2×D97 | #95 | semidirect |
| 120. C97 | C22⋊#95 | semidirect |
| 131. C23×C4 | #87604 | semidirect |
| 202. C2×C4 | C22⋊#87604 | semidirect |
| 221. C22 | (C2×#87604)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#87604 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| C23×C4×D97 | 2 |
| C22⋊#95 | 97 |