Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
256 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C24×C17 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C23×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C17×#106 | C2 | semidirect |
| 5. C17×#340 | C2 | semidirect |
| 6. C17×#340 | C2 | semidirect |
| 7. C17×#340 | C2 | semidirect |
| 85. #2077 | C17 | direct (N × H) |
| 109. C2×#106 | C2×C17 | semidirect |
| 113. #340 | C2×C17 | semidirect |
| 114. #340 | C2×C17 | semidirect |
| 115. #340 | C2×C17 | semidirect |
| 137. C17 | #2077 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×#106 | 2 |
| C2×C17×C22⋊C8 | 2 |
| C17×#380 | 2 |
| C17×#340 | 2 |
| #2077 | 17 |