Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
500 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D17 |
| commutator, socle | C22×C17 | C23×C4 |
| Fitting, prime radical | C17×#532 | C2 |
| cosocle | C2×C4×C17 | C24 |
| hypercenter | #532 | D17 |
| hypocenter | C17 | #2931 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587634 | C2 | semidirect |
| 2. #11762887 | C2 | semidirect |
| 3. D4×#3622 | C2 | semidirect |
| 4. #11762833 | C2 | semidirect |
| 5. #11762776 | C2 | semidirect |
| 6. C2×C4×#3622 | C2 | semidirect |
| 43. C2×#3622 | D4 | semidirect |
| 77. C4×C17 | #131 | semidirect |
| 108. C17 | #2931 | semidirect |
| 160. C4 | #10587634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587634 | 2 |
| #11762887 | 2 |
| D4×#3622 | 2 |
| #11762833 | 2 |
| #11762776 | 2 |
| C2×C4×#3622 | 2 |
| C17×#532 | 2 |
| #2931 | 17 |