Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
440 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C23 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C25×C17 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ 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. C17×#407 | C2 | semidirect |
| 3. C17×#323 | C2 | semidirect |
| 13. C17×C22⋊C8 | C22 | semidirect |
| 50. C23×C17 | M16 | semidirect |
| 63. #1462 | C17 | direct (N × H) |
| 86. #407 | C2×C17 | semidirect |
| 87. #323 | C2×C17 | semidirect |
| 104. C22⋊C8 | C22×C17 | semidirect |
| 105. C17 | #1462 | direct (N × H) |
| 142. C23 | M16×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊C4×C17 | 2 |
| C17×#407 | 2 |
| C17×#323 | 2 |
| #1462 | 17 |