Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
804 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 153 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×#392 | C2 |
| hypercenter | #392 | D17 |
| hypocenter | C17 | #2656 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587570 | C2 | semidirect |
| 2. C2×#10587624 | C2 | semidirect |
| 3. #11762746 | C2 | semidirect |
| 4. #11762745 | C2 | semidirect |
| 5. #11762717 | C2 | semidirect |
| 6. #95×D17 | C2 | semidirect |
| 7. C17×#392 | C2 | semidirect |
| 37. C2×C4×D17 | D4 | semidirect |
| 91. #392 | D17 | semidirect |
| 113. C17 | #2656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587570 | 2 |
| C2×#10587624 | 2 |
| #11762746 | 2 |
| #11762745 | 2 |
| #11762717 | 2 |
| #95×D17 | 2 |
| C17×#392 | 2 |
| #2656 | 17 |