Finite Group DatabasebetaFinite Group DatabasebetaOrder 30592.
456 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 144 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×C239 | C2×D4 |
| commutator | C2×C4 | C22×C4×C239 |
| Frattini, cosocle | C22×C4 | C23×C239 |
| prime radical | C2×#121×C239 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C239 ◁ C23×C4×C239 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C4⋊C4×C239 | C2 | semidirect |
| 3. C2×#102×C239 | C2 | semidirect |
| 4. C2×C22⋊C8×C239 | C2 | semidirect |
| 5. #340×C239 | C2 | semidirect |
| 12. #121×C239 | C4 | semidirect |
| 28. C2×D4×C239 | C2×C4 | semidirect |
| 46. C4⋊C4×C239 | C2×C4 | semidirect |
| 47. C4⋊C4×C239 | D4 | semidirect |
| 97. C22×C239 | #102 | semidirect |
| 119. C239 | #1874 | direct (N × H) |
| 120. #1874 | C239 | direct (N × H) |
| 122. C22×C4⋊C4 | C2×C239 | semidirect |
| 123. C2×#102 | C2×C239 | semidirect |
| 124. C2×C22⋊C8 | C2×C239 | semidirect |
| 125. #340 | C2×C239 | semidirect |
| 132. #121 | C4×C239 | semidirect |
| 148. C2×D4 | C2×C4×C239 | semidirect |
| 166. C4⋊C4 | C2×C4×C239 | semidirect |
| 167. C4⋊C4 | D4×C239 | semidirect |
| 217. C22 | #102×C239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#121×C239 | 2 |
| C22×C4⋊C4×C239 | 2 |
| C2×#102×C239 | 2 |
| C2×C22⋊C8×C239 | 2 |
| #340×C239 | 2 |
| #1874 | 239 |