Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
212 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 68 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×C97 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C97 |
| prime radical | #555×C97 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C97 ◁ C42×C97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #487×C97 | C2 | semidirect |
| 3. #474×C97 | C2 | semidirect |
| 4. #461×C97 | C2 | semidirect |
| 5. #333×C97 | C2 | semidirect |
| 6. D4⋊C8×C97 | C2 | semidirect |
| 7. D4⋊C8×C97 | C2 | semidirect |
| 93. #1646 | C97 | direct (N × H) |
| 94. C97 | #1646 | direct (N × H) |
| 96. #487 | C2×C97 | semidirect |
| 97. #474 | C2×C97 | semidirect |
| 98. #461 | C2×C97 | semidirect |
| 99. #333 | C2×C97 | semidirect |
| 100. D4⋊C8 | C2×C97 | semidirect |
| 101. D4⋊C8 | C2×C97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #555×C97 | 2 |
| #487×C97 | 2 |
| #474×C97 | 2 |
| #461×C97 | 2 |
| #333×C97 | 2 |
| D4⋊C8×C97 | 2 |
| #1646 | 97 |