Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
256 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #121 |
| commutator | C2×C4 | C22×C4×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| socle | C2×C17 | #380 |
| prime radical | C2×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C17×#108 | C2 | semidirect |
| 3. C17×#427 | C2 | semidirect |
| 5. C17×#344 | C2 | semidirect |
| 9. C17×#131 | C4 | semidirect |
| 10. C17×#131 | C4 | semidirect |
| 74. #1814 | C17 | direct (N × H) |
| 88. C2×#108 | C2×C17 | semidirect |
| 89. #427 | C2×C17 | semidirect |
| 91. #344 | C2×C17 | semidirect |
| 100. #131 | C4×C17 | semidirect |
| 101. #131 | C4×C17 | semidirect |
| 113. C17 | #1814 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C17×#131 | 2 |
| C2×C17×#108 | 2 |
| C17×#427 | 2 |
| C17×#421 | 2 |
| C17×#344 | 2 |
| #1814 | 17 |