Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
816 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 258 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 |
|---|---|---|
| 3. C2×#10587549 | C2 | direct (N × H) |
| 6. C22×Q8×C17 | C4 | semidirect |
| 9. C2×Q8×D17 | C4 | semidirect |
| 14. C22×Dic34 | C4 | semidirect |
| 20. #10587549 | C22 | direct (N × H) |
| 25. C2×Q8×C17 | C2×C4 | semidirect |
| 33. Q8×D17 | C2×C4 | semidirect |
| 44. C2×Dic34 | C2×C4 | semidirect |
| 58. Q8×C17 | C22×C4 | semidirect |
| 75. Dic34 | C22×C4 | semidirect |
| 78. C22×C17 | #103 | semidirect |
| 80. C2×D17 | #103 | semidirect |
| 96. C2×C17 | C2×#103 | semidirect |
| 98. D17 | C2×#103 | semidirect |
| 107. C22×Q8 | #595 | semidirect |
| 117. C17 | C22×#103 | semidirect |
| 129. C2×Q8 | C2×#595 | semidirect |
| 157. Q8 | C22×#595 | semidirect |
| 179. C22 | #10587549 | direct (N × H) |
| 191. C2 | C2×#10587549 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#63242 | 2 |
| C22×C4⋊#595 | 2 |
| C2×#10587549 | 2 |
| C22×Q8×D17 | 2 |
| C22×#103 | 17 |