Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
126 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 59 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, prime radical | C22×C17 | C22×C8 |
| Fitting | C4⋊C4×C17 | C8 |
| cosocle | C2×#3624 | C23 |
| hypercenter | C4⋊C4 | #3633 |
| hypocenter | C17 | #2183 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 27. #63241 | Q8 | semidirect |
| 78. C17 | #2183 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11763912 | 2 |
| C4⋊#63241 | 2 |
| #11763903 | 2 |
| C4×#63241 | 2 |
| #11763858 | 2 |
| #2183 | 17 |