Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
162 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #117 |
| commutator | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| socle | C2×C17 | #383 |
| prime radical | C23×C17 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C2×M16×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C17×#97 | C4 | semidirect |
| 12. C4×C8×C17 | C4 | semidirect |
| 40. #1841 | C17 | direct (N × H) |
| 63. #97 | C4×C17 | semidirect |
| 64. C4×C8 | C4×C17 | semidirect |
| 65. C17 | #1841 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×M16×C17 | 2 |
| C17×#344 | 2 |
| C17×#339 | 2 |
| C17×#338 | 2 |
| C17×H(3,ℤ/4) | 2 |
| #1841 | 17 |