Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
708 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C24 |
| Fitting, prime radical | C2×C17×#121 | C2 |
| hypercenter | C2×#121 | D17 |
| hypocenter | C17 | #2501 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587621 | C2 | semidirect |
| 2. C22×C4⋊Dic17 | C2 | semidirect |
| 3. #11762745 | C2 | semidirect |
| 4. #11762712 | C2 | semidirect |
| 5. #11762678 | C2 | semidirect |
| 6. C4×C22⋊Dic17 | C2 | semidirect |
| 42. C22⋊Dic17 | D4 | semidirect |
| 86. C4×C17 | #123 | semidirect |
| 118. C17 | #2501 | semidirect |
| 182. C4 | #10587621 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587621 | 2 |
| C22×C4⋊Dic17 | 2 |
| #11762745 | 2 |
| #11762712 | 2 |
| #11762678 | 2 |
| C4×C22⋊Dic17 | 2 |
| C2×C17×#121 | 2 |
| #2501 | 17 |