Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 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×#10587499 | C2 | direct (N × H) |
| 3. C22×#63214 | C2 | semidirect |
| 4. C22×Q16×C17 | C2 | semidirect |
| 8. C2×Q16×C17 | C22 | semidirect |
| 12. #10587499 | C22 | direct (N × H) |
| 13. C2×#63214 | C22 | semidirect |
| 22. Q16×C17 | C23 | semidirect |
| 27. #63214 | C23 | semidirect |
| 41. C22×C17 | SD32 | semidirect |
| 48. C22×Q16 | D17 | semidirect |
| 52. C2×C17 | C2×SD32 | semidirect |
| 58. C2×Q16 | C2×D17 | semidirect |
| 64. C17 | C22×SD32 | semidirect |
| 73. Q16 | C22×D17 | semidirect |
| 93. C22 | #10587499 | direct (N × H) |
| 99. C2 | C2×#10587499 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D136 | 2 |
| C2×#10587499 | 2 |
| C22×#63214 | 2 |
| C22×Q16×C17 | 2 |
| C22×SD32 | 17 |