Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 78 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×C73 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C73 |
| prime radical | C73×#2206 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C42×C73 ◁ C82×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C73×#2208 | C2 | semidirect |
| 3. C73×#1709 | C2 | semidirect |
| 4. C73×#1589 | C2 | semidirect |
| 5. C73×#1367 | C2 | semidirect |
| 6. C73×#1362 | C2 | semidirect |
| 7. C73×#1361 | C2 | semidirect |
| 113. #12495 | C73 | direct (N × H) |
| 119. #2208 | C2×C73 | semidirect |
| 121. #1709 | C2×C73 | semidirect |
| 122. #1589 | C2×C73 | semidirect |
| 123. #1367 | C2×C73 | semidirect |
| 124. #1362 | C2×C73 | semidirect |
| 125. #1361 | C2×C73 | semidirect |
| 126. C73 | #12495 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#2208 | 2 |
| C73×#2206 | 2 |
| C73×#1709 | 2 |
| C73×#1589 | 2 |
| C73×#1367 | 2 |
| C73×#1362 | 2 |
| C73×#1361 | 2 |
| #12495 | 73 |