Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
440 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 274 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. Q8×#3624 | C2 | direct (N × H) |
| 14. C2×Q8×C17 | C8 | semidirect |
| 20. C2×#3624 | Q8 | direct (N × H) |
| 27. Q8×C17 | C2×C8 | semidirect |
| 37. #3624 | C2×Q8 | direct (N × H) |
| 52. C2×C17 | C8×Q8 | semidirect |
| 65. C17 | C2×C8×Q8 | semidirect |
| 66. C2×Q8 | #3624 | direct (N × H) |
| 79. Q8 | C2×#3624 | direct (N × H) |
| 99. C2 | Q8×#3624 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#3624 | 2 |
| C2×C4⋊#3624 | 2 |
| C2×C4×#3624 | 2 |
| C2×Q8×Dic17 | 2 |
| C2×C8×Q8 | 17 |