Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1334 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 290 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C67 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C67 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C67 ◁ C22×C4×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C67×#3573 | C2 | semidirect |
| 2. C67×#3058 | C2 | semidirect |
| 3. C67×#3027 | C2 | semidirect |
| 4. C67×#1910 | C2 | semidirect |
| 5. C67×#1812 | C2 | semidirect |
| 7. C22×D8×C67 | C22 | semidirect |
| 16. #427×C67 | C22 | semidirect |
| 17. #418×C67 | C22 | semidirect |
| 19. H(3,ℤ/4)×C67 | C22 | semidirect |
| 35. C2×M16×C67 | D4 | semidirect |
| 38. C22×C8×C67 | D4 | semidirect |
| 116. #32948 | C67 | direct (N × H) |
| 121. #3573 | C2×C67 | semidirect |
| 122. #3058 | C2×C67 | semidirect |
| 123. #3027 | C2×C67 | semidirect |
| 124. #1910 | C2×C67 | semidirect |
| 125. #1812 | C2×C67 | semidirect |
| 126. C67 | #32948 | direct (N × H) |
| 128. C22×D8 | C22×C67 | semidirect |
| 137. #427 | C22×C67 | semidirect |
| 138. #418 | C22×C67 | semidirect |
| 140. H(3,ℤ/4) | C22×C67 | semidirect |
| 156. C2×M16 | D4×C67 | semidirect |
| 159. C22×C8 | D4×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#3573 | 2 |
| C67×#3058 | 2 |
| C67×#3027 | 2 |
| C67×#1910 | 2 |
| C67×#1812 | 2 |
| #32948 | 67 |