Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
788 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 788 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 | C17×#384 | C2 |
| hypercenter | #384 | D17 |
| hypocenter | C17 | #2537 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10587581 | C2 | semidirect |
| 2. C2×C4×D68 | C2 | semidirect |
| 3. #11762726 | C2 | semidirect |
| 4. #11762666 | C2 | semidirect |
| 5. C17×#384 | C2 | semidirect |
| 27. C2×D68 | D4 | semidirect |
| 33. C42×C17 | D4 | semidirect |
| 74. C4×C17 | #121 | semidirect |
| 79. #384 | D17 | semidirect |
| 99. C17 | #2537 | semidirect |
| 118. C42 | D68 | semidirect |
| 156. C4 | #10587581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587581 | 2 |
| C2×C4×D68 | 2 |
| #11762726 | 2 |
| #11762666 | 2 |
| C17×#384 | 2 |
| #2537 | 17 |