Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
112 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 28 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 | AΣL(1,𝔽16) |
| commutator | C2×D4 | C2×C4×C17 |
| Frattini, cosocle | #124 | C22×C17 |
| prime radical | C17×H(5,𝔽2) | C4 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×C4×C17 ◁ C17×#124 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#355 | C2 | semidirect |
| 3. C17×#329 | C2 | semidirect |
| 40. #1403 | C17 | direct (N × H) |
| 51. #355 | C2×C17 | semidirect |
| 52. #329 | C2×C17 | semidirect |
| 64. C17 | #1403 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#455 | 2 |
| C17×#355 | 2 |
| C17×#329 | 2 |
| #1403 | 17 |