Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
276 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 73 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. #11763922 | C2 | semidirect |
| 2. C2×C4×#3633 | C2 | semidirect |
| 3. Q8⋊#3633 | C2 | semidirect |
| 4. D4⋊#3633 | C2 | semidirect |
| 30. #41×C17 | C8 | semidirect |
| 31. #63256 | C8 | semidirect |
| 34. #63254 | C8 | semidirect |
| 38. #63252 | C8 | semidirect |
| 69. Q8×C17 | C2×C8 | semidirect |
| 71. D4×C17 | C2×C8 | semidirect |
| 80. D68 | C2×C8 | semidirect |
| 89. Dic34 | C2×C8 | semidirect |
| 141. C17 | #1476 | semidirect |
| 147. #41 | #3633 | semidirect |
| 178. Q8 | C2×#3633 | semidirect |
| 185. D4 | C2×#3633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763922 | 2 |
| C2×C4×#3633 | 2 |
| Q8⋊#3633 | 2 |
| D4⋊#3633 | 2 |
| #41×#595 | 2 |
| #1476 | 17 |