Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
164 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×#10587538 | C2 | semidirect |
| 2. C22×#63216 | C2 | semidirect |
| 3. C4⋊#63216 | C2 | semidirect |
| 4. C22⋊#63216 | C2 | semidirect |
| 5. C22⋊#63216 | C2 | semidirect |
| 6. #11763697 | C2 | semidirect |
| 39. #63216 | D4 | semidirect |
| 63. C22×C17 | M32 | semidirect |
| 96. C17 | #2168 | semidirect |
| 138. C22 | #10587538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587538 | 2 |
| C22×#63216 | 2 |
| C4⋊#63216 | 2 |
| C22⋊#63216 | 2 |
| #11763697 | 2 |
| D4×#3622 | 2 |
| #2168 | 17 |