Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
368 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. #11763212 | C2 | semidirect |
| 3. #11763188 | C2 | semidirect |
| 4. #11763161 | C2 | semidirect |
| 5. #11763159 | C2 | semidirect |
| 7. C4×#63231 | C2 | semidirect |
| 73. C2×C4×C17 | Q16 | semidirect |
| 139. C17 | #3170 | semidirect |
| 182. C2×C4 | #63231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763366 | 2 |
| #11763212 | 2 |
| #11763188 | 2 |
| #11763161 | 2 |
| #11763159 | 2 |
| #11763048 | 2 |
| C4×#63231 | 2 |
| C2×C4×#3622 | 2 |
| C17×#533 | 2 |
| #3170 | 17 |