Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
400 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 181 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. #11762871 | C2 | semidirect |
| 3. #11762860 | C2 | semidirect |
| 4. #11762837 | C2 | semidirect |
| 6. C2×C4×#3622 | C2 | semidirect |
| 7. C4×M16×C17 | C2 | semidirect |
| 79. C4×M16 | D17 | semidirect |
| 101. C17 | #2922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#63252 | 2 |
| #11762871 | 2 |
| #11762860 | 2 |
| #11762837 | 2 |
| #11762777 | 2 |
| C2×C4×#3622 | 2 |
| C4×M16×C17 | 2 |
| #2922 | 17 |