Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
442 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 120 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 | C2×C22⋊C4 |
| prime radical | C17×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C42×C17 | C2 | semidirect |
| 3. C2×C17×#104 | C2 | semidirect |
| 4. C17×#407 | C2 | semidirect |
| 5. C17×#339 | C2 | semidirect |
| 11. C17×C22⋊Q8 | C4 | semidirect |
| 12. C17×#121 | C4 | semidirect |
| 24. C2×Q8×C17 | C2×C4 | semidirect |
| 27. C2×D4×C17 | C2×C4 | semidirect |
| 42. C4⋊C4×C17 | C2×C4 | semidirect |
| 49. C42×C17 | D4 | semidirect |
| 77. #1896 | C17 | direct (N × H) |
| 85. C22×C17 | #104 | semidirect |
| 96. C22×C42 | C2×C17 | semidirect |
| 97. C2×#104 | C2×C17 | semidirect |
| 98. #407 | C2×C17 | semidirect |
| 99. #339 | C2×C17 | semidirect |
| 111. C22⋊Q8 | C4×C17 | semidirect |
| 112. #121 | C4×C17 | semidirect |
| 121. C17 | #1896 | direct (N × H) |
| 125. C2×Q8 | C2×C4×C17 | semidirect |
| 128. C2×D4 | C2×C4×C17 | semidirect |
| 143. C4⋊C4 | C2×C4×C17 | semidirect |
| 150. C42 | D4×C17 | semidirect |
| 185. C22 | C17×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#525 | 2 |
| C22×C42×C17 | 2 |
| C2×C17×#104 | 2 |
| C17×#407 | 2 |
| C17×#339 | 2 |
| #1896 | 17 |