Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
388 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C2×D4 |
| commutator | C4 | C2×C42×C17 |
| Frattini, cosocle | C22×C4 | C23×C17 |
| prime radical | C22×D4×C17 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C17×#97 | C2 | semidirect |
| 4. C4×C4⋊C4×C17 | C2 | semidirect |
| 5. C17×#340 | C2 | semidirect |
| 10. C4×D4×C17 | C4 | semidirect |
| 16. C17×#102 | C4 | semidirect |
| 33. C2×C8×C17 | C2×C4 | semidirect |
| 37. C4⋊C4×C17 | C2×C4 | semidirect |
| 50. D4×C17 | C42 | semidirect |
| 67. #1762 | C17 | direct (N × H) |
| 87. C2×#97 | C2×C17 | semidirect |
| 88. C4×C4⋊C4 | C2×C17 | semidirect |
| 89. #340 | C2×C17 | semidirect |
| 100. C4×D4 | C4×C17 | semidirect |
| 106. #102 | C4×C17 | semidirect |
| 109. C17 | #1762 | direct (N × H) |
| 124. C2×C8 | C2×C4×C17 | semidirect |
| 128. C4⋊C4 | C2×C4×C17 | semidirect |
| 141. D4 | C42×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C17 | 2 |
| C2×C17×#102 | 2 |
| C2×C17×#97 | 2 |
| C4×C4⋊C4×C17 | 2 |
| C17×#340 | 2 |
| #1762 | 17 |