Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
330 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 124 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×#4223)⋊C4 | C2 | direct (N × H) |
| 7. C22×#4223 | C4 | semidirect |
| 9. C22×C4×C41 | C4 | semidirect |
| 10. C22×Dic41 | C4 | semidirect |
| 12. C2×C4×D41 | C4 | semidirect |
| 24. C2×#4223 | C2×C4 | semidirect |
| 26. C2×C4×C41 | C2×C4 | semidirect |
| 28. C2×Dic41 | C2×C4 | semidirect |
| 47. C2×C41 | #95 | semidirect |
| 51. D41 | #95 | semidirect |
| 55. C41 | C2×#95 | semidirect |
| 68. C22×C4 | #4223 | semidirect |
| 85. C2×C4 | C2×#4223 | semidirect |
| 105. C2 | (C2×#4223)⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#4223 | 2 |
| (C2×#4223)⋊C4 | 2 |
| C22×C4×D41 | 2 |
| C2×#95 | 41 |