Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
284 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 92 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 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C17×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C17×C22⋊C8 | C2 | semidirect |
| 3. C17×#381 | C2 | semidirect |
| 4. C17×#328 | C2 | semidirect |
| 5. C17×#327 | C2 | semidirect |
| 6. C2×#41×C17 | C4 | semidirect |
| 10. C17×C22⋊Q8 | C4 | semidirect |
| 12. C17×#121 | C4 | semidirect |
| 17. C17×#117 | C4 | semidirect |
| 82. #1516 | C17 | direct (N × H) |
| 106. C2×C22⋊C8 | C2×C17 | semidirect |
| 107. #381 | C2×C17 | semidirect |
| 108. #328 | C2×C17 | semidirect |
| 109. #327 | C2×C17 | semidirect |
| 117. C2×#41 | C4×C17 | semidirect |
| 121. C22⋊Q8 | C4×C17 | semidirect |
| 123. #121 | C4×C17 | semidirect |
| 128. #117 | C4×C17 | semidirect |
| 134. C17 | #1516 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#525 | 2 |
| C2×C17×C22⋊C8 | 2 |
| C17×#381 | 2 |
| C17×#328 | 2 |
| C17×#327 | 2 |
| #1516 | 17 |