Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
212 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 212 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 | C22×C17 | #121 |
| commutator | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C23×C17 | #41 |
| 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 |
|---|---|---|
| 21. C17×#101 | C4 | semidirect |
| 75. #1930 | C17 | direct (N × H) |
| 114. #101 | C4×C17 | semidirect |
| 117. C17 | #1930 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#428 | 2 |
| C17×#419 | 2 |
| C2×C17×#103 | 2 |
| C2×C17×#101 | 2 |
| C17×#405 | 2 |
| C17×#343 | 2 |
| C17×#341 | 2 |
| #1930 | 17 |