Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
356 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| socle | C22×C17 | C22×D4 |
| prime radical | C23×C17 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#500 | C2 | semidirect |
| 3. C17×#499 | C2 | semidirect |
| 4. C17×#498 | C2 | semidirect |
| 22. C2×C8×C17 | Q8 | semidirect |
| 44. #3160 | C17 | direct (N × H) |
| 54. #500 | C2×C17 | semidirect |
| 55. #499 | C2×C17 | semidirect |
| 56. #498 | C2×C17 | semidirect |
| 74. C17 | #3160 | direct (N × H) |
| 78. C2×C8 | Q8×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#533 | 2 |
| C17×#500 | 2 |
| C17×#499 | 2 |
| C17×#498 | 2 |
| C17×#427 | 2 |
| C2×C4×C8×C17 | 2 |
| #3160 | 17 |