Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C23×C17 |
| prime radical | C17×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C17×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C17×SD32 | C2 | semidirect |
| 2. C17×#504 | C2 | semidirect |
| 3. C17×#473 | C2 | semidirect |
| 5. C17×#368 | C2 | semidirect |
| 6. C17×#362 | C2 | semidirect |
| 7. C17×#361 | C2 | semidirect |
| 59. #2223 | C17 | direct (N × H) |
| 68. C2×SD32 | C2×C17 | semidirect |
| 69. #504 | C2×C17 | semidirect |
| 70. #473 | C2×C17 | semidirect |
| 72. #368 | C2×C17 | semidirect |
| 73. #362 | C2×C17 | semidirect |
| 74. #361 | C2×C17 | semidirect |
| 94. C17 | #2223 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×SD32 | 2 |
| C17×#504 | 2 |
| C17×#473 | 2 |
| C17×#472 | 2 |
| C17×#368 | 2 |
| C17×#362 | 2 |
| C17×#361 | 2 |
| #2223 | 17 |