Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
196 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C8×C17 | C22 |
| commutator | C2 | C2×C4×C8×C17 |
| Frattini, cosocle | C2×C8 | C23×C17 |
| socle | C22×C17 | C22×C8 |
| prime radical | C23×C17 | C2×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C8×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C17×#346 | C2 | semidirect |
| 4. C4×C16×C17 | C2 | semidirect |
| 8. C17×M32 | C4 | direct (N × H) |
| 25. C16×C17 | C2×C4 | semidirect |
| 38. C4×M32 | C17 | direct (N × H) |
| 44. C4×C17 | M32 | direct (N × H) |
| 49. #346 | C2×C17 | semidirect |
| 50. C4×C16 | C2×C17 | semidirect |
| 57. M32 | C4×C17 | direct (N × H) |
| 63. C17 | C4×M32 | direct (N × H) |
| 75. C16 | C2×C4×C17 | semidirect |
| 93. C4 | C17×M32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×M32 | 2 |
| C2×C4×C8×C17 | 2 |
| C17×#346 | 2 |
| C4×C16×C17 | 2 |
| C4×M32 | 17 |