Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
332 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #121 |
| commutator | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C2×C17×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C17×#131 | C2 | semidirect |
| 3. C17×#417 | C2 | semidirect |
| 4. C2×C17×#102 | C2 | semidirect |
| 5. C2×C17×#100 | C2 | semidirect |
| 6. C17×#343 | C2 | semidirect |
| 7. C17×#341 | C2 | semidirect |
| 11. C17×AGL(1,ℤ/8) | C4 | semidirect |
| 97. #1907 | C17 | direct (N × H) |
| 118. C2×#131 | C2×C17 | semidirect |
| 119. #417 | C2×C17 | semidirect |
| 120. C2×#102 | C2×C17 | semidirect |
| 121. C2×#100 | C2×C17 | semidirect |
| 122. #343 | C2×C17 | semidirect |
| 123. #341 | C2×C17 | semidirect |
| 134. AGL(1,ℤ/8) | C4×C17 | semidirect |
| 151. C17 | #1907 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×AGL(1,ℤ/8) | 2 |
| C2×C17×#131 | 2 |
| C17×#417 | 2 |
| C2×C17×#102 | 2 |
| C2×C17×#100 | 2 |
| C17×#343 | 2 |
| C17×#341 | 2 |
| #1907 | 17 |