Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
884 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 884 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 |
| 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×#2657 | C2 | semidirect |
| 2. C67×#2644 | C2 | semidirect |
| 3. C67×#2042 | C2 | semidirect |
| 4. C67×#2041 | C2 | semidirect |
| 5. C67×#2012 | C2 | semidirect |
| 6. C67×#2011 | C2 | semidirect |
| 7. C67×#1840 | C2 | semidirect |
| 146. #32802 | C67 | direct (N × H) |
| 152. #2657 | C2×C67 | semidirect |
| 153. #2644 | C2×C67 | semidirect |
| 154. #2042 | C2×C67 | semidirect |
| 155. #2041 | C2×C67 | semidirect |
| 156. #2012 | C2×C67 | semidirect |
| 157. #2011 | C2×C67 | semidirect |
| 158. #1840 | C2×C67 | semidirect |
| 159. C67 | #32802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#2657 | 2 |
| C67×#2644 | 2 |
| C67×#2042 | 2 |
| C67×#2041 | 2 |
| C67×#2012 | 2 |
| C67×#2011 | 2 |
| C67×#1840 | 2 |
| #32802 | 67 |