Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
164 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#3633 |
| commutator, socle | C22×C17 | C22×C8 |
| Fitting, prime radical | C2×D4×C17 | C8 |
| cosocle | C2×#3624 | C23 |
| hypercenter | C2×D4 | #3633 |
| hypocenter | C17 | #2168 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587670 | C2 | semidirect |
| 2. C22×#63241 | C2 | semidirect |
| 3. #11763912 | C2 | semidirect |
| 4. C22⋊#63241 | C2 | semidirect |
| 5. C22⋊#63241 | C2 | semidirect |
| 6. #11763903 | C2 | semidirect |
| 35. #63241 | D4 | semidirect |
| 63. C22×C17 | M32 | semidirect |
| 96. C17 | #2168 | semidirect |
| 138. C22 | #10587670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587670 | 2 |
| C22×#63241 | 2 |
| #11763912 | 2 |
| C22⋊#63241 | 2 |
| #11763903 | 2 |
| D4×#3624 | 2 |
| #2168 | 17 |