Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
1072 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 389 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. C23×#3622 | C2 | semidirect |
| 2. C22×C4⋊Dic17 | C2 | semidirect |
| 3. C2×#10587503 | C2 | direct (N × H) |
| 8. C22×D4×C17 | C4 | semidirect |
| 13. C2×C4⋊Dic17 | C22 | semidirect |
| 15. C22×#3622 | C22 | semidirect |
| 16. #10587503 | C22 | direct (N × H) |
| 25. C2×D4×C17 | C2×C4 | semidirect |
| 34. C4⋊Dic17 | C23 | semidirect |
| 36. C2×#3622 | C23 | semidirect |
| 48. D4×C17 | C22×C4 | semidirect |
| 62. C22×C17 | #102 | semidirect |
| 76. C2×C17 | C2×#102 | semidirect |
| 83. C22×D4 | Dic17 | semidirect |
| 92. C17 | C22×#102 | semidirect |
| 101. C2×D4 | C2×Dic17 | semidirect |
| 124. D4 | C22×Dic17 | semidirect |
| 137. C22 | #10587503 | direct (N × H) |
| 147. C2 | C2×#10587503 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3622 | 2 |
| C22×C4⋊Dic17 | 2 |
| C2×#10587503 | 2 |
| C23×D4×C17 | 2 |
| C22×#102 | 17 |