Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
410 conjugacy classes of subgroups; only the 256 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 256 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 | C22 | C23×C4×C17 |
| Frattini, cosocle | C2×C4 | C24×C17 |
| socle | C22×C17 | C23×C4 |
| prime radical | C17×#532 | C2 |
| 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 |
|---|---|---|
| 2. C17×#436 | C2 | semidirect |
| 3. C8×D4×C17 | C2 | semidirect |
| 4. C17×#431 | C2 | semidirect |
| 5. C17×#408 | C2 | semidirect |
| 56. #2979 | C17 | direct (N × H) |
| 69. #436 | C2×C17 | semidirect |
| 70. C8×D4 | C2×C17 | semidirect |
| 71. #431 | C2×C17 | semidirect |
| 72. #408 | C2×C17 | semidirect |
| 91. C17 | #2979 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#532 | 2 |
| C17×#436 | 2 |
| C8×D4×C17 | 2 |
| C17×#431 | 2 |
| C17×#408 | 2 |
| #2979 | 17 |