Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
440 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 228 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. #11763858 | C2 | semidirect |
| 2. Q8×#3624 | C2 | semidirect |
| 20. Q8×D17 | C8 | semidirect |
| 28. #63242 | Q8 | direct (N × H) |
| 37. Q8×C17 | C2×C8 | semidirect |
| 48. Dic34 | C2×C8 | semidirect |
| 50. #3624 | C2×Q8 | semidirect |
| 71. D17 | C8×Q8 | semidirect |
| 85. C17 | C2×C8×Q8 | semidirect |
| 105. Q8 | #63242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763858 | 2 |
| Q8×#3624 | 2 |
| #11763810 | 2 |
| C4×#63242 | 2 |
| C4×Q8×D17 | 2 |
| C2×C8×Q8 | 17 |