Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
114 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #327 |
| commutator | C2×C8 | C2×C4×C17 |
| Frattini, cosocle | C2×M16 | C22×C17 |
| prime radical | C17×#469 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×M16×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#349 | C2 | semidirect |
| 3. C17×H(3,ℤ/4) | C2 | semidirect |
| 4. C2×D8×C17 | C4 | semidirect |
| 9. C17×#106 | C4 | semidirect |
| 37. #1339 | C17 | direct (N × H) |
| 50. #349 | C2×C17 | semidirect |
| 51. H(3,ℤ/4) | C2×C17 | semidirect |
| 56. C2×D8 | C4×C17 | semidirect |
| 61. #106 | C4×C17 | semidirect |
| 63. C17 | #1339 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#469 | 2 |
| C17×#349 | 2 |
| C17×H(3,ℤ/4) | 2 |
| #1339 | 17 |