Finite Group DatabasebetaFinite Group DatabasebetaOrder 7808.
348 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 136 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×C61 | C2×D4 |
| commutator | C2×C4 | C22×C4×C61 |
| Frattini, cosocle | C22×C4 | C23×C61 |
| prime radical | C22×D4×C61 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C2×C42×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#106×C61 | C2 | semidirect |
| 3. C2×#103×C61 | C2 | semidirect |
| 5. C2×C4×C8×C61 | C2 | semidirect |
| 6. C61×#391 | C2 | semidirect |
| 12. C2×SD16×C61 | C4 | semidirect |
| 79. C2×C4×C61 | SD16 | semidirect |
| 87. C8×C61 | C22⋊C4 | semidirect |
| 106. #1968 | C61 | direct (N × H) |
| 114. C2×#106 | C2×C61 | semidirect |
| 115. C2×#103 | C2×C61 | semidirect |
| 117. C2×C4×C8 | C2×C61 | semidirect |
| 118. #391 | C2×C61 | semidirect |
| 120. C61 | #1968 | direct (N × H) |
| 125. C2×SD16 | C4×C61 | semidirect |
| 192. C2×C4 | SD16×C61 | semidirect |
| 200. C8 | C22⋊C4×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD16×C61 | 2 |
| C2×#106×C61 | 2 |
| C2×#103×C61 | 2 |
| C2×#102×C61 | 2 |
| C2×C4×C8×C61 | 2 |
| C61×#391 | 2 |
| C61×#390 | 2 |
| #1968 | 61 |