Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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 | semidirect |
| 3. #11763899 | C2 | semidirect |
| 4. Q8⋊#3633 | C2 | semidirect |
| 6. #11763893 | C2 | semidirect |
| 39. SD16×C17 | C8 | semidirect |
| 40. #63230 | C8 | semidirect |
| 41. #63229 | C8 | semidirect |
| 42. #63219 | C8 | semidirect |
| 56. Q8×C17 | C2×C8 | semidirect |
| 63. Dic34 | C2×C8 | semidirect |
| 65. C8×C17 | C2×C8 | semidirect |
| 66. #3622 | C2×C8 | semidirect |
| 109. C17 | SD16⋊C8 | semidirect |
| 116. SD16 | #3633 | semidirect |
| 134. Q8 | C2×#3633 | semidirect |
| 153. C8 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#3633 | 2 |
| D4×#3633 | 2 |
| #11763899 | 2 |
| Q8⋊#3633 | 2 |
| D4⋊#3633 | 2 |
| #11763893 | 2 |
| SD16×#595 | 2 |
| SD16⋊C8 | 17 |