Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
440 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 215 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×#3633 | C2 | direct (N × H) |
| 17. C2×#3633 | Q8 | direct (N × H) |
| 20. C2×Q8×C17 | C8 | semidirect |
| 21. Q8×D17 | C8 | semidirect |
| 24. C2×Dic34 | C8 | semidirect |
| 36. #3633 | C2×Q8 | direct (N × H) |
| 37. Q8×C17 | C2×C8 | semidirect |
| 42. Dic34 | C2×C8 | semidirect |
| 59. C2×C17 | C8×Q8 | semidirect |
| 61. D17 | C8×Q8 | semidirect |
| 73. C17 | C2×C8×Q8 | semidirect |
| 77. C2×Q8 | #3633 | direct (N × H) |
| 90. Q8 | C2×#3633 | direct (N × H) |
| 117. C2 | Q8×#3633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#3633 | 2 |
| C2×C4⋊#3633 | 2 |
| C2×C4×#3633 | 2 |
| C2×Q8×#595 | 2 |
| C2×C8×Q8 | 17 |