Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
276 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | D4 |
| commutator | C4 | C22×C8×C17 |
| Frattini, cosocle | C42 | C23×C17 |
| socle | C22×C17 | C2×C22⋊C4 |
| prime radical | C2×#41×C17 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ C2×C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#431 | C2 | semidirect |
| 3. C2×C4×C8×C17 | C2 | semidirect |
| 4. C17×Q8⋊C8 | C2 | semidirect |
| 5. C17×D4⋊C8 | C2 | semidirect |
| 24. #41×C17 | C8 | semidirect |
| 54. Q8×C17 | C2×C8 | semidirect |
| 57. D4×C17 | C2×C8 | semidirect |
| 76. #1476 | C17 | direct (N × H) |
| 95. #431 | C2×C17 | semidirect |
| 96. C2×C4×C8 | C2×C17 | semidirect |
| 97. Q8⋊C8 | C2×C17 | semidirect |
| 98. D4⋊C8 | C2×C17 | semidirect |
| 121. C17 | #1476 | direct (N × H) |
| 123. #41 | C8×C17 | semidirect |
| 153. Q8 | C2×C8×C17 | semidirect |
| 156. D4 | C2×C8×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#41×C17 | 2 |
| C17×#431 | 2 |
| C2×C4×C8×C17 | 2 |
| C17×Q8⋊C8 | 2 |
| C17×D4⋊C8 | 2 |
| #1476 | 17 |