Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
336 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
| 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 |
|---|---|---|
| 1. D42×C97 | C2 | semidirect |
| 2. #493×C97 | C2 | semidirect |
| 3. #459×C97 | C2 | semidirect |
| 4. #331×C97 | C2 | semidirect |
| 5. D4⋊C8×C97 | C2 | semidirect |
| 10. #127×C97 | C22 | semidirect |
| 14. C4⋊C8×C97 | C22 | semidirect |
| 16. C4×C8×C97 | C22 | semidirect |
| 48. D4×C97 | D8 | semidirect |
| 74. #1619 | C97 | direct (N × H) |
| 75. C97 | #1619 | direct (N × H) |
| 76. D42 | C2×C97 | semidirect |
| 77. #493 | C2×C97 | semidirect |
| 78. #459 | C2×C97 | semidirect |
| 79. #331 | C2×C97 | semidirect |
| 80. D4⋊C8 | C2×C97 | semidirect |
| 85. #127 | C22×C97 | semidirect |
| 89. C4⋊C8 | C22×C97 | semidirect |
| 91. C4×C8 | C22×C97 | semidirect |
| 123. D4 | D8×C97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D42×C97 | 2 |
| #493×C97 | 2 |
| #459×C97 | 2 |
| #331×C97 | 2 |
| D4⋊C8×C97 | 2 |
| #1619 | 97 |