Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
226 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 72 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 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C17 |
| prime radical | C17×#466 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C22×C8×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Q16×C17 | C2 | semidirect |
| 2. C2×C17×SD32 | C2 | semidirect |
| 4. C17×#358 | C2 | semidirect |
| 5. C17×C22⋊C16 | C2 | semidirect |
| 27. Q16×C17 | D4 | semidirect |
| 52. #2185 | C17 | direct (N × H) |
| 58. C22×C17 | SD32 | semidirect |
| 65. C22×Q16 | C2×C17 | semidirect |
| 66. C2×SD32 | C2×C17 | semidirect |
| 68. #358 | C2×C17 | semidirect |
| 69. C22⋊C16 | C2×C17 | semidirect |
| 86. C17 | #2185 | direct (N × H) |
| 97. Q16 | D4×C17 | semidirect |
| 127. C22 | C17×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×C17 | 2 |
| C2×C17×SD32 | 2 |
| C17×#466 | 2 |
| C17×#358 | 2 |
| C17×C22⋊C16 | 2 |
| #2185 | 17 |