Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
768 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| prime radical | C22×D8×C67 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ #376×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C67×#2658 | C2 | semidirect |
| 2. C67×#2644 | C2 | semidirect |
| 3. C67×#2043 | C2 | semidirect |
| 4. C67×#2042 | C2 | semidirect |
| 5. C67×#2013 | C2 | semidirect |
| 7. C67×#1840 | C2 | semidirect |
| 134. #32804 | C67 | direct (N × H) |
| 140. #2658 | C2×C67 | semidirect |
| 141. #2644 | C2×C67 | semidirect |
| 142. #2043 | C2×C67 | semidirect |
| 143. #2042 | C2×C67 | semidirect |
| 144. #2013 | C2×C67 | semidirect |
| 146. #1840 | C2×C67 | semidirect |
| 147. C67 | #32804 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#2658 | 2 |
| C67×#2644 | 2 |
| C67×#2043 | 2 |
| C67×#2042 | 2 |
| C67×#2013 | 2 |
| C67×#2012 | 2 |
| C67×#1840 | 2 |
| #32804 | 67 |