Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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 | C17×#401 | C2 |
| prime radical | C23×D17 | C23 |
| hypercenter | #401 | D17 |
| hypocenter | C17 | #2834 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #401 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17⋊#401 | C2 | semidirect |
| 3. #11762743 | C2 | semidirect |
| 4. #11762741 | C2 | semidirect |
| 7. C17×#401 | C2 | semidirect |
| 67. #401 | D17 | semidirect |
| 90. C17 | #2834 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17⋊#401 | 2 |
| #11762746 | 2 |
| #11762743 | 2 |
| #11762741 | 2 |
| #11762738 | 2 |
| #11762683 | 2 |
| C17×#401 | 2 |
| #2834 | 17 |