Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
308 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C17 |
| prime radical | D42×C17 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C17×#486 | C2 | semidirect |
| 3. C17×#474 | C2 | semidirect |
| 4. C17×#461 | C2 | semidirect |
| 5. C17×#331 | C2 | semidirect |
| 6. C17×D4⋊C8 | C2 | semidirect |
| 7. C17×D4⋊C8 | C2 | semidirect |
| 11. C17×C4⋊Q8 | C22 | semidirect |
| 19. C17×C4⋊C8 | C22 | semidirect |
| 20. C17×C4⋊C8 | C22 | semidirect |
| 24. C4×C8×C17 | C22 | semidirect |
| 70. D4×C17 | SD16 | semidirect |
| 84. #1639 | C17 | direct (N × H) |
| 105. #486 | C2×C17 | semidirect |
| 106. #474 | C2×C17 | semidirect |
| 107. #461 | C2×C17 | semidirect |
| 108. #331 | C2×C17 | semidirect |
| 109. D4⋊C8 | C2×C17 | semidirect |
| 110. D4⋊C8 | C2×C17 | semidirect |
| 120. C4⋊Q8 | C22×C17 | semidirect |
| 128. C4⋊C8 | C22×C17 | semidirect |
| 129. C4⋊C8 | C22×C17 | semidirect |
| 133. C4×C8 | C22×C17 | semidirect |
| 134. C17 | #1639 | direct (N × H) |
| 180. D4 | SD16×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D42×C17 | 2 |
| C17×#486 | 2 |
| C17×#474 | 2 |
| C17×#461 | 2 |
| C17×#331 | 2 |
| C17×D4⋊C8 | 2 |
| #1639 | 17 |