Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
402 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 108 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×C97 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C97 |
| prime radical | C2×#127×C97 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C97 ◁ C2×C42×C97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#102×C97 | C2 | semidirect |
| 3. C2×#102×C97 | C2 | semidirect |
| 4. #389×C97 | C2 | semidirect |
| 5. #336×C97 | C2 | semidirect |
| 42. C4⋊C4×C97 | D4 | semidirect |
| 103. #2041 | C97 | direct (N × H) |
| 104. C97 | #2041 | direct (N × H) |
| 106. C2×#102 | C2×C97 | semidirect |
| 107. C2×#102 | C2×C97 | semidirect |
| 108. #389 | C2×C97 | semidirect |
| 109. #336 | C2×C97 | semidirect |
| 146. C4⋊C4 | D4×C97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#127×C97 | 2 |
| C2×#102×C97 | 2 |
| #389×C97 | 2 |
| #336×C97 | 2 |
| #2041 | 97 |