Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
206 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 206 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 |
| prime radical | C17×#578 | 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 |
|---|---|---|
| 2. C17×#510 | C2 | semidirect |
| 3. C2×C17×Q32 | C2 | semidirect |
| 4. C17×#473 | C2 | semidirect |
| 5. C17×#362 | C2 | semidirect |
| 6. C17×#359 | C2 | semidirect |
| 7. C17×#350 | C2 | semidirect |
| 75. #2195 | C17 | direct (N × H) |
| 86. #510 | C2×C17 | semidirect |
| 87. C2×Q32 | C2×C17 | semidirect |
| 88. #473 | C2×C17 | semidirect |
| 89. #362 | C2×C17 | semidirect |
| 90. #359 | C2×C17 | semidirect |
| 91. #350 | C2×C17 | semidirect |
| 113. C17 | #2195 | 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×#510 | 2 |
| C2×C17×Q32 | 2 |
| C17×#473 | 2 |
| C17×#362 | 2 |
| C17×#359 | 2 |
| C17×#350 | 2 |
| #2195 | 17 |