Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
210 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 64 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 | #447 |
| commutator, Frattini, cosocle | C2×C8 | C23×C17 |
| 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. C17×#578 | C2 | semidirect |
| 2. C17×#509 | C2 | semidirect |
| 3. C2×C17×SD32 | C2 | semidirect |
| 4. C17×#472 | C2 | semidirect |
| 5. C17×#362 | C2 | semidirect |
| 6. C17×#359 | C2 | semidirect |
| 7. C17×#350 | C2 | semidirect |
| 75. #2193 | C17 | direct (N × H) |
| 86. #578 | C2×C17 | semidirect |
| 87. #509 | C2×C17 | semidirect |
| 88. C2×SD32 | C2×C17 | semidirect |
| 89. #472 | C2×C17 | semidirect |
| 90. #362 | C2×C17 | semidirect |
| 91. #359 | C2×C17 | semidirect |
| 92. #350 | C2×C17 | semidirect |
| 115. C17 | #2193 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#578 | 2 |
| C17×#509 | 2 |
| C2×C17×SD32 | 2 |
| C17×#472 | 2 |
| C17×#362 | 2 |
| C17×#359 | 2 |
| C17×#350 | 2 |
| #2193 | 17 |