Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
906 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C67 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C67 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C2×C42×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C67×#3567 | C2 | semidirect |
| 2. C67×#3217 | C2 | semidirect |
| 3. C67×#1658 | C2 | semidirect |
| 4. C67×#1656 | C2 | semidirect |
| 5. C67×#1535 | C2 | semidirect |
| 6. #564×C67 | C22 | semidirect |
| 7. #562×C67 | C22 | semidirect |
| 21. #330×C67 | C22 | semidirect |
| 22. #329×C67 | C22 | semidirect |
| 136. #19096 | C67 | direct (N × H) |
| 141. #3567 | C2×C67 | semidirect |
| 142. #3217 | C2×C67 | semidirect |
| 143. #1658 | C2×C67 | semidirect |
| 144. #1656 | C2×C67 | semidirect |
| 145. #1535 | C2×C67 | semidirect |
| 146. C67 | #19096 | direct (N × H) |
| 147. #564 | C22×C67 | semidirect |
| 148. #562 | C22×C67 | semidirect |
| 162. #330 | C22×C67 | semidirect |
| 163. #329 | C22×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#3567 | 2 |
| C67×#3217 | 2 |
| C67×#1658 | 2 |
| C67×#1656 | 2 |
| C67×#1535 | 2 |
| #19096 | 67 |