Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
380 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C23×C17 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×#575 | C2 | semidirect |
| 2. C2×C17×AGL(1,ℤ/8) | C2 | semidirect |
| 3. C17×#535 | C2 | semidirect |
| 4. C17×#421 | C2 | semidirect |
| 5. C17×#418 | C2 | semidirect |
| 6. C17×#410 | C2 | semidirect |
| 7. C17×#344 | C2 | semidirect |
| 41. C2×Q8×C17 | D4 | semidirect |
| 52. C2×D4×C17 | D4 | semidirect |
| 65. M16×C17 | D4 | semidirect |
| 67. C2×C8×C17 | D4 | semidirect |
| 115. #2008 | C17 | direct (N × H) |
| 136. #575 | C2×C17 | semidirect |
| 137. C2×AGL(1,ℤ/8) | C2×C17 | semidirect |
| 138. #535 | C2×C17 | semidirect |
| 139. #421 | C2×C17 | semidirect |
| 140. #418 | C2×C17 | semidirect |
| 141. #410 | C2×C17 | semidirect |
| 142. #344 | C2×C17 | semidirect |
| 173. C17 | #2008 | direct (N × H) |
| 184. C2×Q8 | D4×C17 | semidirect |
| 195. C2×D4 | D4×C17 | semidirect |
| 208. M16 | D4×C17 | semidirect |
| 210. C2×C8 | D4×C17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×#575 | 2 |
| C2×C17×AGL(1,ℤ/8) | 2 |
| C17×#535 | 2 |
| C17×#421 | 2 |
| C17×#418 | 2 |
| C17×#410 | 2 |
| C17×#344 | 2 |
| #2008 | 17 |