Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
280 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #3633 |
| commutator, hypocenter | C17 | C2×C82 |
| Frattini | C4 | C22×#3633 |
| Fitting | C2×C8×C17 | C8 |
| socle | C22×C17 | C4×C8 |
| prime radical | C22×D17 | C42 |
| cosocle | C4×#595 | C23 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C8×#3633 | C2 | direct (N × H) |
| 13. C2×#3633 | C8 | direct (N × H) |
| 16. C2×#3624 | C8 | semidirect |
| 20. #63242 | C8 | semidirect |
| 22. C2×C8×C17 | C8 | semidirect |
| 23. C2×#3622 | C8 | semidirect |
| 24. C8×D17 | C8 | semidirect |
| 30. #3633 | C2×C8 | direct (N × H) |
| 37. #3624 | C2×C8 | semidirect |
| 38. C8×C17 | C2×C8 | semidirect |
| 39. #3622 | C2×C8 | semidirect |
| 54. C2×C17 | C82 | semidirect |
| 56. D17 | C82 | semidirect |
| 66. C17 | C2×C82 | semidirect |
| 77. C2×C8 | #3633 | direct (N × H) |
| 94. C8 | C2×#3633 | direct (N × H) |
| 107. C2 | C8×#3633 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#3633 | 2 |
| C8×#3633 | 2 |
| C2×C8×#595 | 2 |
| C2×C82 | 17 |