Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
132 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 60 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 | C23×C17 | D8 |
| 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 |
|---|---|---|
| 3. C17×#367 | C2 | semidirect |
| 4. C17×#366 | C2 | semidirect |
| 5. C17×#358 | C2 | semidirect |
| 6. C17×#358 | C2 | semidirect |
| 50. #2237 | C17 | direct (N × H) |
| 64. #367 | C2×C17 | semidirect |
| 65. #366 | C2×C17 | semidirect |
| 66. #358 | C2×C17 | semidirect |
| 67. #358 | C2×C17 | semidirect |
| 84. C17 | #2237 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#467 | 2 |
| C17×#427 | 2 |
| C17×#367 | 2 |
| C17×#366 | 2 |
| C17×#358 | 2 |
| C17×C22⋊C16 | 2 |
| #2237 | 17 |