Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
930 conjugacy classes of subgroups; only the 760 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 760 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 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C17 |
| socle | C22×C17 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#564 | C2 | semidirect |
| 2. C17×#563 | C2 | semidirect |
| 3. C17×#562 | C2 | semidirect |
| 4. C17×#533 | C2 | semidirect |
| 5. C17×#529 | C2 | semidirect |
| 43. #3531 | C17 | direct (N × H) |
| 51. #564 | C2×C17 | semidirect |
| 52. #563 | C2×C17 | semidirect |
| 53. #562 | C2×C17 | semidirect |
| 54. #533 | C2×C17 | semidirect |
| 55. #529 | C2×C17 | semidirect |
| 73. C17 | #3531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#564 | 2 |
| C17×#563 | 2 |
| C17×#562 | 2 |
| C17×#533 | 2 |
| C17×#529 | 2 |
| #3531 | 17 |