Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
752 conjugacy classes of subgroups; only the 246 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 246 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 |
|---|---|---|
| 7. C2×C4×#87604 | C4 | semidirect |
| 8. (C2×#87604)⋊C4 | C4 | semidirect |
| 10. #15690717 | C4 | semidirect |
| 11. #95×C97 | C4 | semidirect |
| 40. C2×#87604 | C42 | semidirect |
| 44. C2×C4×C97 | C42 | semidirect |
| 46. C2×Dic97 | C42 | semidirect |
| 63. #87604 | #95 | direct (N × H) |
| 74. C97 | C4×#95 | semidirect |
| 85. #95 | #87604 | direct (N × H) |
| 123. C2×C4 | C4×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#87604 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| #95×D97 | 2 |
| C4×#95 | 97 |