Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
564 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 114 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C73 |
| prime radical | C73×#3205 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C73×#3208 | C2 | semidirect |
| 3. C73×#3135 | C2 | semidirect |
| 4. C73×#1961 | C2 | semidirect |
| 5. C73×#1518 | C2 | semidirect |
| 6. C73×#1517 | C2 | semidirect |
| 7. C73×#1281 | C2 | semidirect |
| 189. #10219 | C73 | direct (N × H) |
| 197. #3208 | C2×C73 | semidirect |
| 199. #3135 | C2×C73 | semidirect |
| 200. #1961 | C2×C73 | semidirect |
| 201. #1518 | C2×C73 | semidirect |
| 202. #1517 | C2×C73 | semidirect |
| 203. #1281 | C2×C73 | semidirect |
| 204. C73 | #10219 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C73×#3208 | 2 |
| C73×#3205 | 2 |
| C73×#3135 | 2 |
| C73×#1961 | 2 |
| C73×#1518 | 2 |
| C73×#1517 | 2 |
| C73×#1281 | 2 |
| #10219 | 73 |