Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
222 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 96 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 | C2×D4 |
| commutator | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| socle | C22×C17 | C4×D4 |
| prime radical | C2×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×C8×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#424 | C2 | semidirect |
| 5. C2×C17×#97 | C2 | semidirect |
| 6. C17×#341 | C2 | semidirect |
| 7. C17×#339 | C2 | semidirect |
| 17. C17×#103 | C4 | semidirect |
| 18. C17×#102 | C4 | semidirect |
| 72. #1938 | C17 | direct (N × H) |
| 86. #424 | C2×C17 | semidirect |
| 90. C2×#97 | C2×C17 | semidirect |
| 91. #341 | C2×C17 | semidirect |
| 92. #339 | C2×C17 | semidirect |
| 107. #103 | C4×C17 | semidirect |
| 108. #102 | C4×C17 | semidirect |
| 111. C17 | #1938 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#424 | 2 |
| C2×C17×#104 | 2 |
| C17×#416 | 2 |
| C17×#408 | 2 |
| C2×C17×#97 | 2 |
| C17×#341 | 2 |
| C17×#339 | 2 |
| #1938 | 17 |