Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
436 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 188 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#532 | C2 | semidirect |
| 2. C17×#474 | C2 | semidirect |
| 3. C17×#466 | C2 | semidirect |
| 4. C17×#459 | C2 | semidirect |
| 5. C2×C17×C4⋊C8 | C2 | semidirect |
| 52. C2×C4×C17 | D8 | semidirect |
| 58. #3245 | C17 | direct (N × H) |
| 72. #532 | C2×C17 | semidirect |
| 73. #474 | C2×C17 | semidirect |
| 74. #466 | C2×C17 | semidirect |
| 75. #459 | C2×C17 | semidirect |
| 76. C2×C4⋊C8 | C2×C17 | semidirect |
| 96. C17 | #3245 | direct (N × H) |
| 129. C2×C4 | D8×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#532 | 2 |
| C17×#474 | 2 |
| C17×#466 | 2 |
| C17×#459 | 2 |
| C2×C17×C4⋊C8 | 2 |
| #3245 | 17 |